---

_________________________＿＿＿＿_＿＿____＿＿________計算コードの具体例___________________________________________
具体例、
1、Legendre 多項式　(コード L-1 )

#include <vector>
using namespace std;


int main()
{
// pn(x)=1/2^n/n! d^n/dx^n (x^2-1)^n
// (n+1)*p(n+1)(x)-(2n+1)*x*pn(x)+n*p(n-1)(x)=0;
// pn(x)=1/2^Σ(-1)^k x^(n-2k) (2n-2k)! /k!/(n-k)!/(n-2k)!
 
//Legendre関数の次数と係数
//Legendre関数の次数 p0,p1...p34

vector<long double >p0(0+1,0.0);
p0[0]=1.0;

vector<long double >p1(1+1,0.0);
p1[0]=0.0;
p1[1]=1.0;

vector<long double >p2(2+1,0.0);
p2[0]=-1/2.0;
p2[1]=0.0;
p2[2]=3/2.0;

vector<long double >p3(3+1,0.0);
p3[0]=0.0;
p3[1]=-3/2.0;
p3[2]=0.0;
p3[3]=5/2.0;

vector<long double >p4(4+1,0.0);
p4[0]=3/8.0;
p4[1]=0.0;
p4[2]=-30/8.0;
p4[3]=0.0;
p4[4]=35/8.0;

vector<long double >p5(5+1,0.0);
p5[0]=0.0;
p5[1]=15.0/8.0;
p5[2]=0.0;
p5[3]=-70.0/8.0;
p5[4]=0.0;
p5[5]=63.0/8.0;

vector<long double >p6(6+1,0.0);
p6[0]=-5.0/16.0;
p6[1]=0.0;
p6[2]=105.0/16.0;
p6[3]=0.0;
p6[4]=-315.0/16.0;
p6[5]=0.0;
p6[6]=231.0/16.0;

vector<long double>p7(7+1,0.0);
p7[0]=0.0;
p7[1]=-35/16.0;
p7[2]=0.0;
p7[3]=315/16.0;
p7[4]=0.0;
p7[5]=-693/16.0;
p7[6]=0.0;
p7[7]=429/16.0;

vector<long double>p8(8+1,0.0);
p8[0]=35/128.0;
p8[1]=0.0;
p8[2]=-315/32.0;
p8[3]=0.0;
p8[4]=3465/64.0;
p8[5]=0.0;
p8[6]=-3003/32.0;
p8[7]=0.0;
p8[8]=6435/128.0;

vector<long double>p9(9+1,0.0);
p9[0]=0.0;
p9[1]=315/128.0;
p9[2]=0.0;
p9[3]=-1155/32.0;
p9[4]=0.0;
p9[5]=9009/64.0;
p9[6]=0.0;
p9[7]=-6435/32.0;
p9[8]=0.0;
p9[9]=12155/128.0;

vector<long double>p10(10+1,0.0);
p10[0]=-63/256.0;
p10[1]=0.0;
p10[2]=3465/256.0;
p10[3]=0.0;
p10[4]=-15015/128.0;
p10[5]=0.0;
p10[6]=45045/128.0;
p10[7]=0.0;
p10[8]=-109395/256.0;
p10[9]=0.0;
p10[10]=46189/256.0;

vector<long double>p11(11+1,0.0);
p11[0]=0.0;
p11[1]=-693/256.0;
p11[2]=0.0;
p11[3]=15015/256.0;
p11[4]=0.0;
p11[5]=-45045/128.0;
p11[6]=0.0;
p11[7]=109395/128.0;
p11[8]=0.0;
p11[9]=-230945/256.0;
p11[10]=0.0;
p11[11]=88179/256.0;

vector<long double>p12(12+1,0.0);
p12[0]=231/1024.0;
p12[1]=0.0;
p12[2]=-9009/512.0;
p12[3]=0.0;
p12[4]=225225/1024.0;
p12[5]=0.0;
p12[6]=-255255/256.0;
p12[7]=0.0;
p12[8]=2078505/1024.0;
p12[9]=0.0;
p12[10]=-969969/512.0;
p12[11]=0.0;
p12[12]=676039/1024.0;

vector<long double>p13(13+1,0.0);
p13[0]=0.0;
p13[1]=3003/1024.0;
p13[2]=0.0;
p13[3]=-45045/512.0;
p13[4]=0.0;
p13[5]=765765/1024.0;
p13[6]=0.0;
p13[7]=-692835/256.0;
p13[8]=0.0;
p13[9]=4849845/1024.0;
p13[10]=0.0;
p13[11]=-2028117/512.0;
p13[12]=0.0;
p13[13]=1300075/1024.0;

vector<long double>p14(14+1,0.0);
p14[0]=-429/2048.0;
p14[1]=0.0;
p14[2]=45045/2048.0;
p14[3]=0.0;
p14[4]=-765765/2048.0;
p14[5]=0.0;
p14[6]=4849845/2048.0;
p14[7]=0.0;
p14[8]=-14549535/2048.0;
p14[9]=0.0;
p14[10]=22309287/2048.0;
p14[11]=0.0;
p14[12]=-16900975/2048.0;
p14[13]=0.0;
p14[14]=5014575/2048.0;

vector<long double>p15(15+1,0.0);
p15[0]=0.0;
p15[1]=-6435/2048.0;
p15[2]=0.0;
p15[3]=255255/2048.0;
p15[4]=0.0;
p15[5]=-2909907/2048.0;
p15[6]=0.0;
p15[7]=14549535/2048.0;
p15[8]=0.0;
p15[9]=-37182145/2048.0;
p15[10]=0.0;
p15[11]=50702925/2048.0;
p15[12]=0.0;
p15[13]=-35102025/2048.0;
p15[14]=0.0;
p15[15]=9694845/2048.0;

vector<long double>p16(16+1,0.0);
p16[0]=6435/32768.0;
p16[1]=0.0;
p16[2]=-109395/4096.0;
p16[3]=0.0;
p16[4]=4849845/8192.0;
p16[5]=0.0;
p16[6]=-20369349/4096.0;
p16[7]=00.0;
p16[8]=334639305/16384.0;
p16[9]=0.0;
p16[10]=-185910725/4096.0;
p16[11]=0.0;
p16[12]=456326325/8192.0;
p16[13]=00.0;
p16[14]=-145422675/4096.0;
p16[15]=0.0;
p16[16]=300540195/32768.0;

vector<long double>p17(17+1,0.0);
p17[0]=	0.0;
p17[1]=	109395/32768.0;
p17[2]=0.0;
p17[3]=	-692835/4096.0;
p17[4]=	0.0;
p17[5]=	20369349/8192.0;
p17[6]=	0.0;
p17[7]=	-66927861/4096.0;
p17[8]=	0.0;
p17[9]=	929553625/16384.0;
p17[10]=0.0;
p17[11]=-456326325/4096.0;
p17[12]=0.0;
p17[13]=1017958725/8192.0;
p17[14]=0.0;
p17[15]=-300540195/4096.0;
p17[16]=0.0;
p17[17]=583401555/32768.0;

vector<long double>p18(18+1,0.0);
p18[0]=-12155/65536.0;
p18[1]=0.0;
p18[2]=2078505/65536.0;
p18[3]=0.0;
p18[4]=-58198140/65536.0;
p18[5]=0.0;
p18[6]=624660036.0/65536.0;
p18[7]=0.0;
p18[8]=-3346393050.0/65536.0;
p18[9]=0.0;
p18[10]=10039179150/65536.0;
p18[11]=0.0;
p18[12]=-17644617900/65536.0;
p18[13]=0.0;
p18[14]=18032411700.0/65536.0;
p18[15]=0.0;
p18[16]=-9917826435.0/65536.0;
p18[17]=0.0;
p18[18]=2268783825/65536.0;

vector<long double>p19(19+1,0.0);
p19[0]=0.0;		
p19[1]=-230945/65536.0;
p19[2]=0.0;		
p19[3]=14549535/65536.0;
p19[4]=0.0;		
p19[5]=-267711444/65536.0;
p19[6]=0.0;		
p19[7]=2230928700/65536.0;
p19[8]=0.0;		
p19[9]=-10039179150/65536.0;
p19[10]=0.0;		
p19[11]=26466926850/65536.0;
p19[12]=0.0;		
p19[13]=-42075627300/65536.0;
p19[14]=0.0;		
p19[15]=39671305740/65536.0;
p19[16]=0.0;		
p19[17]=-20419054425/65536.0;
p19[18]=0.0;		
p19[19]=4418157975/65536.0;

vector<long double>p20(20+1,0.0);
p20[0]=46189/262144.0;
p20[1]=0.0;		
p20[2]=-9699690/262144.0;
p20[3]=0.0;		
p20[4]=334639305/262144.0;
p20[5]=0.0;		
p20[6]=-4461857400/262144.0;
p20[7]=0.0;		
p20[8]=30117537450/262144.0;
p20[9]=0.0;		
p20[10]=-116454478140/262144.0;
p20[11]=0.0;		
p20[12]=273491577450/262144.0;
p20[13]=0.0;		
p20[14]=-396713057400/262144.0;
p20[15]=0.0;		
p20[16]=347123925225/262144.0;
p20[17]=0.0;		
p20[18]=-167890003050/262144.0;
p20[19]=0.0;		
p20[20]=34461632205/262144.0;

vector<long double>p21(21+1,0.0);
p21[0]=0.0;		
p21[1]=969969/262144.0;
p21[2]=0.0;		
p21[3]=-74364290/262144.0;
p21[4]=0.0;		
p21[5]=1673196525/262144.0;
p21[6]=0.0;		
p21[7]=-17210021400/262144.0;
p21[8]=0.0;		
p21[9]=97045398450/262144.0;
p21[10]=0.0;		
p21[11]=-328189892940/262144.0;
p21[12]=0.0;		
p21[13]=694247850450/262144.0;
p21[14]=0.0;		
p21[15]=-925663800600/262144.0;
p21[16]=0.0;		
p21[17]=755505013725/262144.0;
p21[18]=0.0;		
p21[19]=-344616322050/262144.0;
p21[20]=0.0;		
p21[21]=67282234305/262144.0;

vector<long double>p22(22+1,0.0);
p22[0]=-88179/524288.0;
p22[1]=0.0;		
p22[2]=22309287/524288.0;
p22[3]=0.0;		
p22[4]=-929553625/524288.0;
p22[5]=0.0;		
p22[6]=15058768725/524288.0;
p22[7]=0.0;		
p22[8]=-124772655150/524288.0;
p22[9]=0.0;		
p22[10]=601681470390/524288.0;
p22[11]=0.0;		
p22[12]=-1805044411170/524288.0;
p22[13]=0.0;		
p22[14]=3471239252250/524288.0;
p22[15]=0.0;		
p22[16]=-4281195077775/524288.0;
p22[17]=0.0;		
p22[18]=3273855059475/524288.0;
p22[19]=0.0;		
p22[20]=-1412926920405/524288.0;
p22[21]=0.0;		
p22[22]=263012370465/524288.0;

vector<long double>p23(23+1,0.0);
p23[0]=0.0;		
p23[1]=-2028117/524288.0;
p23[2]=0.0;		
p23[3]=185910725/524288.0;
p23[4]=0.0;		
p23[5]=-5019589575/524288.0;
p23[6]=0.0;		
p23[7]=62386327575/524288.0;
p23[8]=0.0;		
p23[9]=-429772478850/524288.0;
p23[10]=0.0;		
p23[11]=1805044411170/524288.0;
p23[12]=0.0;		
p23[13]=-4859734953150/524288.0;
p23[14]=0.0;		
p23[15]=8562390155550/524288.0;
p23[16]=0.0;		
p23[17]=-9821565178425/524288.0;
p23[18]=0.0;		
p23[19]=7064634602025/524288.0;
p23[20]=0.0;		
p23[21]=-2893136075115/524288.0;
p23[22]=0.0;		
p23[23]=514589420475/524288.0;

vector<long double>p24(24+1,0.0);
p24[0]=676039/4194304.0;//2^22
p24[1]=0.0;		
p24[2]=-202811700/4194304.0;
p24[3]=0.0;		
p24[4]=10039179150/4194304.0;
p24[5]=0.0;		
p24[6]=-194090796900/4194304.0;
p24[7]=0.0;		
p24[8]=1933976154825/4194304.0;
p24[9]=0.0;		
p24[10]=-11345993441640/4194304.0;
p24[11]=0.0;		
p24[12]=42117702927300/4194304.0;
p24[13]=0.0;		
p24[14]=-102748681866600/4194304.0;
p24[15]=0.0;		
p24[16]=166966608033225/4194304.0;
p24[17]=0.0;		
p24[18]=-178970743251300/4194304.0;
p24[19]=0.0;		
p24[20]=121511715154830/4194304.0;
p24[21]=0.0;		
p24[22]=-47342226683700/4194304.0;
p24[23]=0.0;		
p24[24]=8061900920775/4194304.0;

vector<long double>p25(25+1,0.0);
p25[0]=0.0;		
p25[1]=16900975/4194304.0;
p25[2]=0.0;		
p25[3]=-1825305300/4194304.0;
p25[4]=0.0;		
p25[5]=58227239070/4194304.0;
p25[6]=0.0;		
p25[7]=-859544957700/4194304.0;
p25[8]=0.0;		
p25[9]=7091245901025/4194304.0;
p25[10]=0.0;		
p25[11]=-36100888223400/4194304.0;
p25[12]=0.0;		
p25[13]=119873462177700/4194304.0;
p25[14]=0.0;		
p25[15]=-267146572853160/4194304.0;
p25[16]=0.0;		
p25[17]=402684172315425/4194304.0;
p25[18]=0.0;		
p25[19]=-405039050516100/4194304.0;
p25[20]=0.0;		
p25[21]=260382246760350/4194304.0;
p25[22]=0.0;		
p25[23]=-96742811049300/4194304.0;
p25[24]=0.0;		
p25[25]=15801325804719/4194304.0;

vector<long double>p26(26+1,0.0);
p26[0]=-1300075/8388608.0;//2^23
p26[1]=0.0;		
p26[2]=456326325/8388608.0;
p26[3]=0.0;		
p26[4]=-26466926850/8388608.0;
p26[5]=0.0;		
p26[6]=601681470390/8388608.0;
p26[7]=0.0;		
p26[8]=-7091245901025/8388608.0;
p26[9]=0.0;		
p26[10]=49638721307175/8388608.0;
p26[11]=0.0;		
p26[12]=-222622144044300/8388608.0;
p26[13]=0.0;		
p26[14]=667866432132900/8388608.00;
p26[15]=0.0;		
p26[16]=-1369126185872445/8388608.0;
p26[17]=0.0;		
p26[18]=1923935489951475/8388608.0;
p26[19]=0.0;		
p26[20]=-1822675727322450/8388608.00;
p26[21]=0.0;		
p26[22]=1112542327066950/8388608.0;
p26[23]=0.0;		
p26[24]=-395033145117975/8388608.0;
p26[25]=0.0;		
p26[26]=61989816618513/8388608.0;

vector<long double>p27(27+1,0.0);
p27[0]=0.0;		
p27[1]=-35102025/8388608.0;//2^23
p27[2]=0.0;		
p27[3]=4411154475/8388608.0;
p27[4]=0.0;		
p27[5]=-164094946470/8388608.0;
p27[6]=0.0;		
p27[7]=2836498360410/8388608.0;
p27[8]=0.0;		
p27[9]=-27577067392875/8388608.0;
p27[10]=0.0;		
p27[11]=166966608033225/8388608.0;
p27[12]=0.0;		
p27[13]=-667866432132900/8388608.0;
p27[14]=0.0;		
p27[15]=1825501581163260/8388608.0;
p27[16]=0.0;		
p27[17]=-3463083881912655/8388608.0;
p27[18]=0.0;		
p27[19]=4556689318306125/8388608.0;
p27[20]=0.0;		
p27[21]=-4079321865912150/8388608.0;
p27[22]=0.0;		
p27[23]=2370198870707850/8388608.0;
p27[24]=0.0;		
p27[25]=-805867616040669/8388608.0;
p27[26]=0.0;		
p27[27]=121683714103007/8388608.0;

vector<long double>p28(28+1,0.0);
p28[0]=5014575/33554432.0;//2^25
p28[1]=0.0;		
p28[2]=-2035917450/33554432.0;
p28[3]=0.0;		
p28[4]=136745788725/33554432.0;
p28[5]=0.0;	
p28[6]=-3610088822340/33554432.0;
p28[7]=0.0;	
p28[8]=49638721307175/33554432.0;
p28[9]=0.0;	
p28[10]=-408140597414550/33554432.0;
p28[11]=0.0;
p28[12]=2170565904431925/33554432.0;
p28[13]=0.0;	
p28[14]=-7823578204985400/33554432.0;
p28[15]=0.0;
p28[16]=19624141997505045/33554432.0;
p28[17]=0.0;		
p28[18]=-34630838819126550/33554432.0;
p28[19]=0.0;		
p28[20]=42832879592077575/33554432.0;
p28[21]=0.0;
p28[22]=-36343049350853700/33554432.0;
p28[23]=0.0;		
p28[24]=20146690401016725/33554432.0;
p28[25]=0.0;		
p28[26]=-6570920561562378/33554432.0;
p28[27]=0.0;		
p28[28]=956086325095055/33554432.0;

vector<long double>p29(29+1,0.0);
p29[0]=0.0;
p29[1]=145422675/33554432.0;
p29[2]=0.0;
p29[3]=-21037813650/33554432.0;
p29[4]=0.0;
p29[5]=902522205585/33554432.0;
p29[6]=0.0;
p29[7]=-18050444111700/33554432.0;
p29[8]=0.0;
p29[9]=204070298707275/33554432.0;
p29[10]=0.0;
p29[11]=-1447043936287950/33554432.0;
p29[12]=0.0;
p29[13]=6845630929362225/33554432.0;
p29[14]=0.0;
p29[15]=-22427590854291480/33554432.0;
p29[16]=0.0;
p29[17]=51946258228689825/33554432.0;
p29[18]=0.0;
p29[19]=-85665759184155150/33554432.0;
p29[20]=0.0;
p29[21]=99943385714847675/33554432.0;
p29[22]=0.0;
p29[23]=-80586761604066900/33554432.0;
p29[24]=0.0;
p29[25]=42710983650155457/33554432.0;
p29[26]=0.0;
p29[27]=-13385208551330770/33554432.0;
p29[28]=0.0;
p29[29]=1879204156221315/33554432.0;

vector<long double>p30(30+1,0.0);
p30[0]=-9694845/67108864.0;
p30[1]=0.0;
p30[2]=4508102925/67108864.0;
p30[3]=0.0;
p30[4]=-347123925225/67108864.0;
p30[5]=0.0;
p30[6]=10529425731825/67108864.0;
p30[7]=0.0;
p30[8]=-166966608033225/67108864.0;
p30[9]=0.0;
p30[10]=1591748329916745/67108864.0;
p30[11]=0.0;
p30[12]=-9888133564634325/67108864.0;
p30[13]=0.0;
p30[14]=42051732851796525/67108864.0;
p30[15]=0.0;
p30[16]=-126155198555389575/67108864.0;
p30[17]=0.0;
p30[18]=271274904083157975/67108864.0;
p30[19]=0.0;
p30[20]=-419762220002360235/67108864.0;
p30[21]=0.0;
p30[22]=463373879223384675/67108864.0;
p30[23]=0.0;
p30[24]=-355924863751295475/67108864.0;
p30[25]=0.0;
p30[26]=180700315442965395/67108864.0;
p30[27]=0.0;
p30[28]=-54496920530418135/67108864.0;
p30[29]=0.0;
p30[30]=7391536347803839/67108864.0;

vector<long double>p31(31+1,0.0);
p31[0]=0.0;
p31[1]=-300540195/67108864.0;//2^26
p31[2]=0.0;
p31[3]=49589132175/67108864.0;
p31[4]=0.0;
p31[5]=-2429867476575/67108864.0;
p31[6]=0.0;
p31[7]=55655536011075/67108864.0;
p31[8]=0.0;
p31[9]=-723521968143975/67108864.0;
p31[10]=0.0;
p31[11]=5932880138780595/67108864.0;
p31[12]=0.0;
p31[13]=-32706903329175075/67108864.0;
p31[14]=0.0;
p31[15]=126155198555389575/67108864.0;
p31[16]=0.0;
p31[17]=-348782019535488825/67108864.0;
p31[18]=0.0;
p31[19]=699603700003933725/67108864.0;
p31[20]=0.0;
p31[21]=-1019422534291446285/67108864.0;
p31[22]=0.0;
p31[23]=1067774591253886425/67108864.0;
p31[24]=0.0;
p31[25]=-783034700252850045/67108864.0;
p31[26]=0.0;
p31[27]=381478443712926945/67108864.0;
p31[28]=0.0;
p31[29]=-110873045217057585/67108864.0;
p31[30]=0.0;
p31[31]=14544636039226909/67108864.0;

vector<long double>p32(32+1,0.0);
p32[0]=300540195/2147483648.0;
p32[1]=0.0;
p32[2]=-9917826435/134217728.0;
p32[3]=0.0;
p32[4]=1735619626125/268435456.0;
p32[5]=0.0;
p32[6]=-29968365544425/134217728.0;
p32[7]=0.0;
p32[8]=2170565904431925/536870912.0;
p32[9]=0.0;
p32[10]=-5932880138780595/134217728.0;
p32[11]=0.0;
p32[12]=85037948655855195/268435456.0;
p32[13]=0.0;
p32[14]=-210258664258982625/134217728.0;
p32[15]=0.0;
p32[16]=5929294332103310025/1073741824.0;
p32[17]=0.0;
p32[18]=-1898924328582105825/134217728.0;
p32[19]=0.0;
p32[20]=7135957740040123995/268435456.0;
p32[21]=0.0;
p32[22]=-4911763119767877555/134217728.0;
p32[23]=0.0;
p32[24]=36462894652.637200;// .6372 以降0が続く 
//p32[24]=78303470025285004500/2147483648;//error C2177:定数が大
p32[25]=0.0;
p32[26]=-3433305993416342505/134217728.0;
p32[27]=0.0;
p32[28]=3215318311294669965/268435456.0;
p32[29]=0.0;
p32[30]=-450883717216034179/134217728.0;
p32[31]=0.0;
p32[32]=916312070471295267/2147483648.0;

vector<long double>p33(33+1,0.0);
p33[0]=0.0;
p33[1]=9917826435/2147483648.0;
p33[2]=0.0;
p33[3]=-115707975075/134217728.0;
p33[4]=0.0;
p33[5]=12843585233325/268435456.0;
p33[6]=0.0;
p33[7]=-166966608033225/134217728.0;
p33[8]=0.0;
p33[9]=9888133564634325/536870912.0;
p33[10]=0.0;
p33[11]=-23192167815233235/134217728.0;
p33[12]=0.0;
p33[13]=294362129962575675/268435456.0;
p33[14]=0.0;
p33[15]=-658810481344812225/134217728.0;
p33[16]=0.0;
p33[17]=17090318957238952425/1073741824.0;
p33[18]=0.0;
p33[19]=-5097112671457231425/134217728.0;
p33[20]=0.0;
p33[21]=18009798105815551035/268435456.0;
p33[22]=0.0;
p33[23]=11745520503792750675/(-134217728.0);
//p33[23]=-11745520503792750675/134217728;//warning:符号型にcast
p33[24]=0.0;
p33[25]=83135399808.012800;// .0128以降0が続く。
//p33[25]=44632977914412452565/536870912;//error C2177:定数が大
p33[26]=0.0;
p33[27]=-7502409393020896585/134217728.0;
p33[28]=0.0;
p33[29]=6763255758240512685/268435456.0;
p33[30]=0.0;
p33[31]=-916312070471295267/134217728.0;
p33[32]=0.0;
p33[33]=1804857108504066435/2147483648.0;

vector<long double>p34(34+1,0.0);
p34[0]=-583401555/4294967296.0;
p34[1]=0.0;
p34[2]=347123925225/4294967296.0;
p34[3]=0.0;
p34[4]=-4281195077775/536870912.0;
p34[5]=0.0;
p34[6]=166966608033225/536870912.0;
p34[7]=0.0;
p34[8]=-6845630929362225/1073741824.0;
p34[9]=0.0;
p34[10]=85037948655855195/1073741824.0;
p34[11]=0.0;
p34[12]=-347882517228498525/536870912.0;
p34[13]=0.0;
p34[14]=1976431444034436675/536870912.0;
p34[15]=0.0;
p34[16]=-15032344304.90800;// .908 以降0が続く。
//p34[16]=-32281713585895799025/2147483648.0;//error C2177:定数が大
p34[17]=0.0;
p34[18]=45097032914.723900;// .7239以降0が続く
//p34[18]=96845140757687397075/2147483648.0;//error C2177:定数が大
p34[19]=0.0;
p34[20]=-100637589241.27900;// .279以降0が続く
//p34[20]=-54029394317446653105/536870912.0;//error C2177:定数が大
p34[21]=0.0;
p34[22]=167729315402.13100;// .131以降0が続く
//p34[22]=90048990529077755175/536870912.0;//error C2177:定数が大
p34[23]=0.0;
p34[24]=-207838499520.03200;// .032以降0が続く
//p34[24]=-223164889572062262825/1073741824.0;//error C2177:定数が大
p34[25]=0.0;
p34[26]=188653407256.64400;// .644以降0が続く
//p34[26]=202565053611564207795/1073741824.0;//error C2177:定数が大
p34[27]=0.0;
p34[28]=-121776273467.252;// .252以降0が続く
//p34[28]=-65378138996324955955/536870912.0;//error C2177:定数が大
p34[29]=0.0;
p34[30]=52909691230.599100;//.5991以降0が続く
//p34[30]=28405674184610153277/536870912.0;//error C2177:定数が大
p34[31]=0.0;
p34[32]=-13867459395.116700;// .1167以降0が続く
//p34[32]=-59560284580634192355/4294967296.0;//error C2177:定数が大
p34[33]=0.0;
p34[34]=7113260368810144185/4294967296.0;

return 0;

}


本章 7章の説明へ


2、Legendre 多項式の直交性確認 (コード　L-2)


#include <cmath>
#include <fstream>
#include <vector>
#include <iomanip>
#include <numeric>
#include <iostream>
#include <string>
#include <sstream>
using namespace std;

#include <direct.h>// for getcwd
const int BUFFSIZE=1000;

const long double PI=3.14159265358979323846264338327950288; 

vector<double> Legendre_function();

vector<double>Newton_Cotes(int div,int j,int m,int n,double x0, double x1,vector<double>fx,
vector<double>gx,vector<double>sum_ini);

int main()
{

//Gauss-Legendre
//2分点
double x20=-1.0/sqrt(3.0);
double x21=1.0/sqrt(3.0);
//重み係数
double wLe2_0=1.0;
double wLe2_1=1.0;


// 以下　次章に記載する　あるいは後日に記載する　ので　削除 


// 以上　次章に記載する　あるいは　後日に追加sする　ので　削除
    

double xCh65=0.86624681810782;
double wCh6=1.0/3.0;

//計算する分割数
vector<int>div0(22,0);

div0[0]=1;
div0[1]=2;
div0[2]=4;
div0[3]=5;
div0[4]=7;

div0[5]=10;
div0[6]=16;
div0[7]=25;
div0[8]=40;
div0[9]=63;

div0[10]=100;
div0[11]=160;

div0[12]=250;
div0[13]=400;
div0[14]=630;

div0[15]=1000;
div0[16]=1600;
div0[17]=2500;
div0[18]=4000;
div0[19]=6300;

div0[20]=10000;
div0[21]=16000;
div0[22]=25000;




//非対角要素の分割数による精度確認 
char dirdata3[BUFFSIZE]; 
_getcwd(dirdata3,BUFFSIZE);
string file_name3="\\accracy_distribution_LegendrePXX_YY.csv";
strcat_s(dirdata3,file_name3.c_str());

fstream out003(dirdata3,ios::out|ios::binary|ios::app);

out003<<"p_"<<"L"<<","<<"div"<<","
        <<"tr_sum"<<","<<"tr more1.0e-2"<<","<<"tr 1.0e-2_1.0e-5"<<","<<"tr 1.0e-5_1.0e-10"
<<","<<"tr 1.0e-10_1.0e-15"<<","<<"tr less than 1.0e-15"<<","
        <<"s3_sum"<<","<<"s3 more1.0e-2"<<","<<"s3 1.0e-2_1.0e-5"<<","<<"s3 1.0e-5_1.0e-10"
<<","<<"s3 1.0e-10_1.0e-15"<<","<<"s3 less than 1.0e-15"<<","
        <<"s8_sum"<<","<<"s8 more1.0e-2"<<","<<"s8 1.0e-2_1.0e-5"<<","<<"s8 1.0e-5_1.0e-10"
<<","<<"s8 1.0e-10_1.0e-15"<<","<<"s8 less than 1.0e-15"<<","
        <<"b4_sum"<<","<<"b4 more1.0e-2"<<","<<"b4 1.0e-2_1.0e-5"<<","<<"b4 1.0e-5_1.0e-10"
<<","<<"b4 1.0e-10_1.0e-15"<<","<<"b4 less than 1.0e-15"<<","<<" "<<","

        
        <<"tr_new_sum"<<","<<"tr_new more1.0e-2"<<","<<"tr_new 1.0e-2_1.0e-5"<<","
<<"tr_new 1.0e-5_1.0e-10"<<","<<"tr_new 1.0e-10_1.0e-15"<<","<<"tr_new less than 1.0e-15"<<","
        <<"s3_new_sum"<<","<<"s3_new more1.0e-2"<<","<<"s3_new 1.0e-2_1.0e-5"<<","
<<"s3_new 1.0e-5_1.0e-10"<<","<<"s3_new 1.0e-10_1.0e-15"<<","<<"s3_new less than 1.0e-15"<<","
        <<"s8_new_sum"<<","<<"s8_new more1.0e-2"<<","<<"s8_new 1.0e-2_1.0e-5"<<","
<<"s8_new 1.0e-5_1.0e-10"<<","<<"s8_new 1.0e-10_1.0e-15"<<","<<"s8_new less than 1.0e-15"<<","
        <<"b4_new_sum"<<","<<"b4_new more1.0e-2"<<","<<"b4_new 1.0e-2_1.0e-5"<<","
<<"b4_new 1.0e-5_1.0e-10"<<","<<"b4_new 1.0e-10_1.0e-15"<<","<<"b4_new less than 1.0e-15"<<","<<" "<<","      

        <<"c5_sum"<<","<<"c5 more1.0e-2"<<","<<"c5 1.0e-2_1.0e-5"<<","<<"c5 1.0e-5_1.0e-10"<<","
<<"c5 1.0e-10_1.0e-15"<<","<<"c5 less than 1.0e-15"<<","
        <<"c6_sum"<<","<<"c6 more1.0e-2"<<","<<"c6 1.0e-2_1.0e-5"<<","<<"c6 1.0e-5_1.0e-10"<<","
<"c6 1.0e-10_1.0e-15"<<","<<"c6 less than 1.0e-15"<<","
        <<"c7_sum"<<","<<"c7 more1.0e-2"<<","<<"c7 1.0e-2_1.0e-5"<<","<<"c7 1.0e-5_1.0e-10"<<","
<<"c7 1.0e-10_1.0e-15"<<","<<"c7 less than 1.0e-15"<<","
        <<"c8_sum"<<","<<"c8 more1.0e-2"<<","<<"c8 1.0e-2_1.0e-5"<<","<<"c8 1.0e-5_1.0e-10"<<","
<<"c8 1.0e-10_1.0e-15"<<","<<"c8 less than 1.0e-15"<<","        
        <<"c9_sum"<<","<<"c9 more1.0e-2"<<","<<"c9 1.0e-2_1.0e-5"<<","<<"c9 1.0e-5_1.0e-10"<<","
<<"c9 1.0e-10_1.0e-15"<<","<<"c9 less than 1.0e-15"<<","
        <<"c10_sum"<<","<<"c10 more1.0e-2"<<","<<"c10 1.0e-2_1.0e-5"<<","<<"c10 1.0e-5_1.0e-10"<<","
<<"c10 1.0e-10_1.0e-15"<<","<<"c10 less than 1.0e-15"<<","<<" "<<","


        <<"Le2_sum"<<","<<"Le2 more1.0e-2"<<","<<"Le2 1.0e-2_1.0e-5"<<","<<"Le2 1.0e-5_1.0e-10"<<","
<<"Le2 1.0e-10_1.0e-15"<<","<<"Le2 less than 1.0e-15"<<","
        <<"Le3_sum"<<","<<"Le3 more1.0e-2"<<","<<"Le3 1.0e-2_1.0e-5"<<","<<"Le3 1.0e-5_1.0e-10"<<","
<<"Le3 1.0e-10_1.0e-15"<<","<<"Le3 less than 1.0e-15"<<","
        <<"Le4_sum"<<","<<"Le4 more1.0e-2"<<","<<"Le4 1.0e-2_1.0e-5"<<","<<"Le4 1.0e-5_1.0e-10"<<","
<<"Le4 1.0e-10_1.0e-15"<<","<<"Le4 less than 1.0e-15"<<","
        <<"Le5_sum"<<","<<"Le5 more1.0e-2"<<","<<"Le5 1.0e-2_1.0e-5"<<","<<"Le5 1.0e-5_1.0e-10"<<","
<<"Le5 1.0e-10_1.0e-15"<<","<<"Le5 less than 1.0e-15"<<","
        <<"Le6_sum"<<","<<"Le6 more1.0e-2"<<","<<"Le6 1.0e-2_1.0e-5"<<","<<"Le6 1.0e-5_1.0e-10"<<","
<<"Le6 1.0e-10_1.0e-15"<<","<<"Le6 less than 1.0e-15"<<","<<" "<<","
        
        <<"Ch2_sum"<<","<<"Ch2 more1.0e-2"<<","<<"Ch2 1.0e-2_1.0e-5"<<","<<"Ch2 1.0e-5_1.0e-10"<<","
<<"Ch2 1.0e-10_1.0e-15"<<","<<"Ch2 less than 1.0e-15"<<","
        <<"Ch3_sum"<<","<<"Ch3 more1.0e-2"<<","<<"Ch3 1.0e-2_1.0e-5"<<","<<"Ch3 1.0e-5_1.0e-10"<<","
<<"Ch3 1.0e-10_1.0e-15"<<","<<"Ch3 less than 1.0e-15"<<","
        <<"Ch4_sum"<<","<<"Ch4 more1.0e-2"<<","<<"Ch4 1.0e-2_1.0e-5"<<","<<"Ch4 1.0e-5_1.0e-10"<<","
<<"Ch4 1.0e-10_1.0e-15"<<","<<"Ch4 less than 1.0e-15"<<","
        <<"Ch5_sum"<<","<<"Ch5 more1.0e-2"<<","<<"Ch5 1.0e-2_1.0e-5"<<","<<"Ch5 1.0e-5_1.0e-10"<<","
<<"Ch5 1.0e-10_1.0e-15"<<","<<"Ch5 less than 1.0e-15"<<","
        <<"Ch6_sum"<<","<<"Ch6 more1.0e-2"<<","<<"Ch6 1.0e-2_1.0e-5"<<","<<"Ch6 1.0e-5_1.0e-10"<<","
<<"Ch6 1.0e-10_1.0e-15"<<","<<"Ch6 less than 1.0e-15"<<","<<" "<<","
        <<endl;
        

double x0=-1.0;
double x1=1.0; 


for(int i=0;i<(int)div0.size();i++)
{
//分割数毎にcsv形式のfile出力を行う準備
stringstream division;
division <<div0[i];
string str = division.str();


char dirdata1[BUFFSIZE]; 
_getcwd(dirdata1,BUFFSIZE);// <direct.h>が必要
string file_end="_div_LegendrePXX_YY.csv";
string file_name="\\"+str+file_end;
strcat_s(dirdata1,file_name.c_str());//ファイル名のdirを生成

fstream out001(dirdata1,ios::out | ios::binary |ios::app);
out001<<"p_"<<"XX"<<"_"<<"YY"<<","<<"div"<<","
        <<"tr_ort/analytic"<<","<<"s3_ort/analytic"<<","<<"s8_ort/analytic"<<","<<"b4_ort/analytic"<<","<<" "<<","
        <<"tr_new/analytic"<<","<<"s3_new/analytic"<<","<<"s8_new/analytic"<<","<<"b4_new/analytic"<<","<<" "<<","
        <<"c5_new/analytic"<<","<<"c6_new/analytic"<<","<<"c7_new/analytic"<<","<<"c8_new/analytic"<<","
<<"c9_new/analytic"<<","<<"c10_new/analytic"<<","<<" "<<","
        <<"Le2_ort/analytic"<<","<<"Le3_ort/analytic"<<","<<"Le4_ort/analytic"<<","<<"Le5_ort/analytic"
<<","<<"Le6_ort/analytic"<<","<<" "<<","
        <<"Ch2_ort/analytic"<<","<<"Ch3_ort/analytic"<<","<<"Ch4_ort/analytic"<<","<<"Ch5_ort/analytic"
<<","<<"Ch6_ort/analytic"<<","<<" "<<","
        <<"analytic_value"<<endl;


char dirdata2[BUFFSIZE]; 
_getcwd(dirdata2,BUFFSIZE);
string file_end2="_div_LegendrePXX_XX.csv";
string file_name2="\\"+str+file_end2;
strcat_s(dirdata2,file_name2.c_str());
fstream out002(dirdata2,ios::out | ios::binary |ios::app);
out002<<"p_"<<"XX"<<"_"<<"XX"<<","<<"div"<<","
        <<"tr_ort/analytic"<<","<<"s3_ort/analytic"<<","<<"s8_ort/analytic"<<","<<"b4_ort/analytic"<<","<<" "<<","
        <<"tr_new/analytic"<<","<<"s3_new/analytic"<<","<<"s8_new/analytic"<<","<<"b4_new/analytic"<<","<<" "<<","
        <<"c5_new/analytic"<<","<<"c6_new/analytic"<<","<<"c7_new/analytic"<<","<<"c8_new/analytic"<<","
<<"c9_new/analytic"<<","<<"c10_new/analytic"<<","<<" "<<","
        <<"Le2_ort/analytic"<<","<<"Le3_ort/analytic"<<","<<"Le4_ort/analytic"<<","<<"Le5_ort/analytic"<<","
<<"Le6_ort/analytic"<<","<<" "<<","
        <<"Ch2_ort/analytic"<<","<<"Ch3_ort/analytic"<<","<<"Ch4_ort/analytic"<<","<<"Ch5_ort/analytic"<<","
<<"Ch6_ort/analytic"<<","<<" "<<","
        <<"analytic_value"<<endl;

//計算結果の精度範囲の個数カウントの初期化 
int ntr2=0;
int ntr2_5=0;
int ntr5_10=0;
int ntr10_15=0;
int ntr15=0;

int ns32=0;
int ns32_5=0;
int ns35_10=0;
int ns310_15=0;
int ns315=0;

int ns82=0;
int ns82_5=0;
int ns85_10=0;
int ns810_15=0;
int ns815=0;

int nb42=0;
int nb42_5=0;
int nb45_10=0;
int nb410_15=0;
int nb415=0;


int ntr_new2=0;
int ntr_new2_5=0;
int ntr_new5_10=0;
int ntr_new10_15=0;
int ntr_new15=0;

int ns3_new2=0;
int ns3_new2_5=0;
int ns3_new5_10=0;
int ns3_new10_15=0;
int ns3_new15=0;

int ns8_new2=0;
int ns8_new2_5=0;
int ns8_new5_10=0;
int ns8_new10_15=0;
int ns8_new15=0;

int nb4_new2=0;
int nb4_new2_5=0;
int nb4_new5_10=0;
int nb4_new10_15=0;
int nb4_new15=0;


int nc52=0;
int nc52_5=0;
int nc55_10=0;
int nc510_15=0;
int nc515=0;

int nc62=0;
int nc62_5=0;
int nc65_10=0;
int nc610_15=0;
int nc615=0;

int nc72=0;
int nc72_5=0;
int nc75_10=0;
int nc710_15=0;
int nc715=0;

int nc82=0;
int nc82_5=0;
int nc85_10=0;
int nc810_15=0;
int nc815=0;

int nc92=0;
int nc92_5=0;
int nc95_10=0;
int nc910_15=0;
int nc915=0;

int nc102=0;
int nc102_5=0;
int nc105_10=0;
int nc1010_15=0;
int nc1015=0;


int nLe22=0;
int nLe22_5=0;
int nLe25_10=0;
int nLe210_15=0;
int nLe215=0;

int nLe32=0;
int nLe32_5=0;
int nLe35_10=0;
int nLe310_15=0;
int nLe315=0;

int nLe42=0;
int nLe42_5=0;
int nLe45_10=0;
int nLe410_15=0;
int nLe415=0;

int nLe52=0;
int nLe52_5=0;
int nLe55_10=0;
int nLe510_15=0;
int nLe515=0;

int nLe62=0;
int nLe62_5=0;
int nLe65_10=0;
int nLe610_15=0;
int nLe615=0;

int nCh22=0;
int nCh22_5=0;
int nCh25_10=0;
int nCh210_15=0;
int nCh215=0;

int nCh32=0;
int nCh32_5=0;
int nCh35_10=0;
int nCh310_15=0;
int nCh315=0;

int nCh42=0;
int nCh42_5=0;
int nCh45_10=0;
int nCh410_15=0;
int nCh415=0;

int nCh52=0;
int nCh52_5=0;
int nCh55_10=0;
int nCh510_15=0;
int nCh515=0;

int nCh62=0;
int nCh62_5=0;
int nCh65_10=0;
int nCh610_15=0;
int nCh615=0;

int tr_sum=0;
int s3_sum=0;
int s8_sum=0;
int b4_sum=0;


int tr_new_sum=0;
int s3_new_sum=0;
int s8_new_sum=0;
int b4_new_sum=0;

int c5_sum=0;
int c6_sum=0;
int c7_sum=0;
int c8_sum=0;
int c9_sum=0;
int c10_sum=0;


int Le2_sum=0;
int Le3_sum=0;
int Le4_sum=0;
int Le5_sum=0;
int Le6_sum=0;
int Ch2_sum=0;
int Ch3_sum=0;
int Ch4_sum=0;
int Ch5_sum=0;
int Ch6_sum=0;


int div=div0[i];

vector<double>hx;
hx=Legendre_function();
hx.resize(hx.size());

vector<double>fx;

vector<double>Cotes(10,0.0);


for(int L=34;L>=0;L--)
{
fx.clear();
int m=L;
for(int i=L*(L+1)/2;i<m+L*(L+1)/2+1;i++) fx.push_back(hx[i]);
fx.resize(fx.size());

vector<double>gx;
for(int k=34;k>=0;k--)
{
gx.clear();
int n=k;
for(int i=k*(k+1)/2;i<n+k*(k+1)/2+1;i++) gx.push_back(hx[i]);
gx.resize(gx.size());


double ana=1.0;//anaは解析値を示す。
if( k==L) ana=2.0/(2.0*L+1);

// output
vector<double> tr_abs(div+1,0.0);// trapezoid 台形則
vector<double> s3_abs(div+1,0.0);// simpson　1/3則 
vector<double> s8_abs(div+1,0.0);// simpson　3/8則
vector<double> b4_abs(div+1,0.0);// Boole則  2/45


vector<double> tr_new_abs(div+1,0.0);// trapezoid 台形則
vector<double> s3_new_abs(div+1,0.0);// simpson　1/3則 
vector<double> s8_new_abs(div+1,0.0);// simpson　3/8則
vector<double> b4_new_abs(div+1,0.0);// Boole則  2/45
vector<double> c5_abs(div+1,0.0);
vector<double> c6_abs(div+1,0.0);
vector<double> c7_abs(div+1,0.0);
vector<double> c8_abs(div+1,0.0);
vector<double> c9_abs(div+1,0.0);
vector<double> c10_abs(div+1,0.0);


vector<double> Le2_abs(div+1,0.0);// Gauss-Legendre 2次 　
vector<double> Le3_abs(div+1,0.0);// Gauss-Legendre 3次
vector<double> Le4_abs(div+1,0.0);// Gauss-Legendre 4次
vector<double> Le5_abs(div+1,0.0);// Gauss-Legendre 5次
vector<double> Le6_abs(div+1,0.0);// Gauss-Legendre 6次

vector<double> Ch2_abs(div+1,0.0);// Chebyshev 2次 
vector<double> Ch3_abs(div+1,0.0);// Chebyshev 3次 
vector<double> Ch4_abs(div+1,0.0);// Chebyshev 4次 
vector<double> Ch5_abs(div+1,0.0);// Chebyshev 5次  
vector<double> Ch6_abs(div+1,0.0);// Chebyshev 6次 


double h=(x1-x0)/div;


double f_xn0=0.0;//分割始点
double f_xn2=0.0;//幅の1/4点
double f_xn3=0.0;//幅の1/3点
double f_xnm=0.0;//中間点
double f_xn6=0.0;//幅の2/3点
double f_xn7=0.0;//幅の3/4点
double f_xn1=0.0;//終点

double g_xn0=0.0;//分割始点
double g_xn2=0.0;//幅の1/4点
double g_xn3=0.0;//幅の1/3点
double g_xnm=0.0;//中間点
double g_xn6=0.0;//幅の2/3点
double g_xn7=0.0;//幅の3/4点
double g_xn1=0.0;//終点




double fg_xn0=0.0;
double fg_xnm=0.0;
double fg_xn1=0.0;

double tr_ort=0.0;// trapezoid 台形則
double s3_ort=0.0;// simpson　1/3則 
double s8_ort=0.0;// simpson　3/8則
double b4_ort=0.0;// Boole則 2/45

vector<double>sum_ini(10,0.0);

double Le2_ort=0.0;// Gauss-Legendre 2次 　
double Le3_ort=0.0;// Gauss-Legendre 3次
double Le4_ort=0.0;// Gauss-Legendre 4次
double Le5_ort=0.0;// Gauss-Legendre 5次
double Le6_ort=0.0;// Gauss-Legendre 6次

double Ch2_ort=0.0;// Chebyshev式 2次 
double Ch3_ort=0.0;// Chebyshev式 3次 
double Ch4_ort=0.0;// Chebyshev式 4次 
double Ch5_ort=0.0;// Chebyshev式 5次  
double Ch6_ort=0.0;// Chebyshev式 6次 



for(int j=0;j<div;j++)
{ 

Cotes=Newton_Cotes(div,j,m,n,x0,x1,fx,gx,sum_ini);
sum_ini=Cotes;


 //台形則、simpson則、Boole則　の積分
 vector<double>p_xn0(m+1,0.0);
 vector<double>p_xn2(m+1,0.0);
 vector<double>p_xn3(m+1,0.0);
 vector<double>p_xnm(m+1,0.0);
 vector<double>p_xn6(m+1,0.0);
 vector<double>p_xn7(m+1,0.0);
 vector<double>p_xn1(m+1,0.0);
 
 vector<double>q_xn0(n+1,0.0);
 vector<double>q_xn2(n+1,0.0);
 vector<double>q_xn3(n+1,0.0);
 vector<double>q_xnm(n+1,0.0);
 vector<double>q_xn6(n+1,0.0);
 vector<double>q_xn7(n+1,0.0);
 vector<double>q_xn1(n+1,0.0); 


  for(int i=0;i<m+1;i++)
 {
         p_xn0[i]=pow(x0+j*h,i);
         p_xn2[i]=pow(x0+j*h+h/4.0,i);
     p_xn3[i]=pow(x0+j*h+h/3.0,i);
         p_xnm[i]=pow(x0+j*h+h/2.0,i);
         p_xn6[i]=pow(x0+j*h+2.0*h/3.0,i);
         p_xn7[i]=pow(x0+j*h+3.0*h/4.0,i);
     p_xn1[i]=pow(x0+j*h+h,i);
 }  
 f_xn0=inner_product(fx.begin(),fx.end(),p_xn0.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn2=inner_product(fx.begin(),fx.end(),p_xn2.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn3=inner_product(fx.begin(),fx.end(),p_xn3.begin(),0.0,plus<double>(),multiplies<double>());
 f_xnm=inner_product(fx.begin(),fx.end(),p_xnm.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn6=inner_product(fx.begin(),fx.end(),p_xn6.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn7=inner_product(fx.begin(),fx.end(),p_xn7.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn1=inner_product(fx.begin(),fx.end(),p_xn1.begin(),0.0,plus<double>(),multiplies<double>());


 for(int i=0;i<n+1;i++)
 {
         q_xn0[i]=pow(x0+j*h,i);
         q_xn2[i]=pow(x0+j*h+h/4.0,i);
     q_xn3[i]=pow(x0+j*h+h/3.0,i);
         q_xnm[i]=pow(x0+j*h+h/2.0,i);
         q_xn6[i]=pow(x0+j*h+2.0*h/3.0,i);
         q_xn7[i]=pow(x0+j*h+3.0*h/4.0,i);
     q_xn1[i]=pow(x0+j*h+h,i);
 }  
 g_xn0=inner_product(gx.begin(),gx.end(),q_xn0.begin(),0.0,plus<double>(),multiplies<double>());
 g_xn2=inner_product(gx.begin(),gx.end(),q_xn2.begin(),0.0,plus<double>(),multiplies<double>());
 g_xn3=inner_product(gx.begin(),gx.end(),q_xn3.begin(),0.0,plus<double>(),multiplies<double>());
 g_xnm=inner_product(gx.begin(),gx.end(),q_xnm.begin(),0.0,plus<double>(),multiplies<double>());
 g_xn6=inner_product(gx.begin(),gx.end(),q_xn6.begin(),0.0,plus<double>(),multiplies<double>());
 g_xn7=inner_product(gx.begin(),gx.end(),q_xn7.begin(),0.0,plus<double>(),multiplies<double>());
 g_xn1=inner_product(gx.begin(),gx.end(),q_xn1.begin(),0.0,plus<double>(),multiplies<double>());

  
 fg_xn0=f_xn0*g_xn0;
 fg_xnm=f_xnm*g_xnm;
 fg_xn1=f_xn1*g_xn1;
 
 tr_ort=tr_ort+(fg_xn0+fg_xn1)*h/2.0;
 s3_ort=s3_ort+(fg_xn0+4.0*fg_xnm+fg_xn1)/3.0*h/2.0;  
 s8_ort=s8_ort+(fg_xn0+3.0*f_xn3*g_xn3+3.0*f_xn6*g_xn6+fg_xn1)*3.0/8.0*h/3.0;
 b4_ort=b4_ort+(7.0*fg_xn0+32.0*f_xn2*g_xn2+12.0*fg_xnm+32.0*f_xn7*g_xn7+7.0*fg_xn1)*2.0/45.0*h/4.0;



//Gauss-Legendre
//2分点
double xLe2_0=x0+j*h+h/2.0+h/2.0*x20;
double xLe2_1=x0+j*h+h/2.0+h/2.0*x21;

double Le2_0=0.0,Le2_1=0.0;
for(int i=0;i<m+1;i++) 
 { 
  Le2_0=Le2_0+fx[i]*pow(xLe2_0,i);
  Le2_1=Le2_1+fx[i]*pow(xLe2_1,i); 
 }

double gLe2_0=0.0,gLe2_1=0.0;
for(int i=0;i<n+1;i++) 
 { 
  gLe2_0=gLe2_0+gx[i]*pow(xLe2_0,i);
  gLe2_1=gLe2_1+gx[i]*pow(xLe2_1,i); 
 }

Le2_ort=Le2_ort+h/2.0*(wLe2_0*Le2_0*gLe2_0+wLe2_1*Le2_1*gLe2_1);


// 以下　次章に記載する　あるいは　後日に追加する　ので　削除


// 以上　削除 

double gCh6_0=0.0,gCh6_1=0.0,gCh6_2=0.0;
double gCh6_3=0.0,gCh6_4=0.0,gCh6_5=0.0;
for(int i=0;i<n+1;i++) 
 { 
  gCh6_0=gCh6_0+gx[i]*pow(xCh6_0,i);
  gCh6_1=gCh6_1+gx[i]*pow(xCh6_1,i);
  gCh6_2=gCh6_2+gx[i]*pow(xCh6_2,i);
  gCh6_3=gCh6_3+gx[i]*pow(xCh6_3,i);
  gCh6_4=gCh6_4+gx[i]*pow(xCh6_4,i);
  gCh6_5=gCh6_5+gx[i]*pow(xCh6_5,i);
 }

Ch6_ort=Ch6_ort+h/2.0*wCh6*(Ch6_0*gCh6_0+Ch6_1*gCh6_1+Ch6_2*gCh6_2+Ch6_3*gCh6_3+Ch6_4*gCh6_4+Ch6_5*gCh6_5);


}//div


if(k==L)
{
out002<<"p_"<<L<<"_"<<k<<","<<div<<","<<setprecision(20)
        <<tr_ort/ana<<","<<s3_ort/ana<<","<<s8_ort/ana<<","<<b4_ort/ana<<","<<" " <<","
        <<Cotes[0]/ana<<","<<Cotes[1]/ana<<","<<Cotes[2]/ana<<","<<Cotes[3]/ana<<","<<" "<<","
        <<Cotes[4]/ana<<","<<Cotes[5]/ana<<","<<Cotes[6]/ana<<","<<Cotes[7]/ana<<","<<Cotes[8]/ana<<","
<<Cotes[9]/ana<<","<<" " <<","
        <<Le2_ort/ana<<","<<Le3_ort/ana<<","<<Le4_ort/ana<<","<<Le5_ort/ana<<","<<Le6_ort/ana<<","<<" "<<","    
        <<Ch2_ort/ana<<","<<Ch3_ort/ana<<","<<Ch4_ort/ana<<","<<Ch5_ort/ana<<","<<Ch6_ort/ana<<","<<" "<<","
        <<ana<<endl;
}
else
{
out001<<"p_"<<L<<"_"<<k<<","<<div<<","<<setprecision(20)
        <<tr_ort/ana<<","<<s3_ort/ana<<","<<s8_ort/ana<<","<<b4_ort/ana<<","<<" "<<","
        <<Cotes[0]/ana<<","<<Cotes[1]/ana<<","<<Cotes[2]/ana<<","<<Cotes[3]/ana<<","<<" "<<","
        <<Cotes[4]/ana<<","<<Cotes[5]/ana<<","<<Cotes[6]/ana<<","<<Cotes[7]/ana<<","<<Cotes[8]/ana<<","
<<Cotes[9]/ana<<","<<" "<<","
        <<Le2_ort/ana<<","<<Le3_ort/ana<<","<<Le4_ort/ana<<","<<Le5_ort/ana<<","<<Le6_ort/ana<<","<<" "<<","
        <<Ch2_ort/ana<<","<<Ch3_ort/ana<<","<<Ch4_ort/ana<<","<<Ch5_ort/ana<<","<<Ch6_ort/ana<<","<<" "<<","
        <<ana<<endl;

if(abs(tr_ort)>=1.0e-2 ) ntr2=ntr2+1;
if(abs(tr_ort)<1.0e-2  && abs(tr_ort)>=1.0e-5) ntr2_5=ntr2_5+1;
if(abs(tr_ort)<1.0e-5 && abs(tr_ort)>=1.0e-10) ntr5_10=ntr5_10+1;
if(abs(tr_ort)<1.0e-10 && abs(tr_ort)>=1.0e-15)ntr10_15=ntr10_15+1;
if(abs(tr_ort)<1.0e-15) ntr15=ntr15+1;
tr_sum=ntr2+ntr2_5+ntr5_10+ntr10_15+ntr15;

if(abs(s3_ort)>=1.0e-2 ) ns32=ns32+1;
if(abs(s3_ort)<1.0e-2  && abs(s3_ort)>=1.0e-5) ns32_5=ns32_5+1;
if(abs(s3_ort)<1.0e-5 && abs(s3_ort)>=1.0e-10) ns35_10=ns35_10+1;
if(abs(s3_ort)<1.0e-10 && abs(s3_ort)>=1.0e-15) ns310_15=ns310_15+1;
if(abs(s3_ort)<1.0e-15) ns315=ns315+1;
s3_sum=ns32+ns32_5+ns35_10+ns310_15+ns315;

if(abs(s8_ort)>=1.0e-2 ) ns82=ns82+1;
if(abs(s8_ort)<1.0e-2  && abs(s8_ort)>=1.0e-5) ns82_5=ns82_5+1;
if(abs(s8_ort)<1.0e-5 && abs(s8_ort)>=1.0e-10) ns85_10=ns85_10+1;
if(abs(s8_ort)<1.0e-10 && abs(s8_ort)>=1.0e-15) ns810_15=ns810_15+1;
if(abs(s8_ort)<1.0e-15) ns815=ns815+1;
s8_sum=ns82+ns82_5+ns85_10+ns810_15+ns815;

if(abs(b4_ort)>=1.0e-2 ) nb42=nb42+1;
if(abs(b4_ort)<1.0e-2  && abs(b4_ort)>=1.0e-5) nb42_5=nb42_5+1;
if(abs(b4_ort)<1.0e-5 && abs(b4_ort)>=1.0e-10) nb45_10=nb45_10+1;
if(abs(b4_ort)<1.0e-10 && abs(b4_ort)>=1.0e-15) nb410_15=nb410_15+1;
if(abs(b4_ort)<1.0e-15) nb415=nb415+1;
b4_sum=nb42+nb42_5+nb45_10+nb410_15+nb415;


if(abs(Cotes[0])>=1.0e-2 ) ntr_new2=ntr_new2+1;
if(abs(Cotes[0])<1.0e-2  && abs(Cotes[0])>=1.0e-5) ntr_new2_5=ntr_new2_5+1;
if(abs(Cotes[0])<1.0e-5 && abs(Cotes[0])>=1.0e-10) ntr_new5_10=ntr_new5_10+1;
if(abs(Cotes[0])<1.0e-10 && abs(Cotes[0])>=1.0e-15)ntr_new10_15=ntr_new10_15+1;
if(abs(Cotes[0])<1.0e-15) ntr_new15=ntr_new15+1;
tr_new_sum=ntr_new2+ntr_new2_5+ntr_new5_10+ntr_new10_15+ntr_new15;

if(abs(Cotes[1])>=1.0e-2 ) ns3_new2=ns3_new2+1;
if(abs(Cotes[1])<1.0e-2  && abs(Cotes[1])>=1.0e-5) ns3_new2_5=ns3_new2_5+1;
if(abs(Cotes[1])<1.0e-5 && abs(Cotes[1])>=1.0e-10) ns3_new5_10=ns3_new5_10+1;
if(abs(Cotes[1])<1.0e-10 && abs(Cotes[1])>=1.0e-15) ns3_new10_15=ns3_new10_15+1;
if(abs(Cotes[1])<1.0e-15) ns3_new15=ns3_new15+1;
s3_new_sum=ns3_new2+ns3_new2_5+ns3_new5_10+ns3_new10_15+ns3_new15;

if(abs(Cotes[2])>=1.0e-2 ) ns8_new2=ns8_new2+1;
if(abs(Cotes[2])<1.0e-2  && abs(Cotes[2])>=1.0e-5) ns8_new2_5=ns8_new2_5+1;
if(abs(Cotes[2])<1.0e-5 && abs(Cotes[2])>=1.0e-10) ns8_new5_10=ns8_new5_10+1;
if(abs(Cotes[2])<1.0e-10 && abs(Cotes[2])>=1.0e-15) ns8_new10_15=ns8_new10_15+1;
if(abs(Cotes[2])<1.0e-15) ns8_new15=ns8_new15+1;
s8_new_sum=ns8_new2+ns8_new2_5+ns8_new5_10+ns8_new10_15+ns8_new15;

if(abs(Cotes[3])>=1.0e-2 ) nb4_new2=nb4_new2+1;
if(abs(Cotes[3])<1.0e-2  && abs(Cotes[3])>=1.0e-5) nb4_new2_5=nb4_new2_5+1;
if(abs(Cotes[3])<1.0e-5 && abs(Cotes[3])>=1.0e-10) nb4_new5_10=nb4_new5_10+1;
if(abs(Cotes[3])<1.0e-10 && abs(Cotes[3])>=1.0e-15) nb4_new10_15=nb4_new10_15+1;
if(abs(Cotes[3])<1.0e-15) nb4_new15=nb4_new15+1;
b4_new_sum=nb4_new2+nb4_new2_5+nb4_new5_10+nb4_new10_15+nb4_new15;


if(abs(Cotes[4])>=1.0e-2 ) nc52=nc52+1;
if(abs(Cotes[4])<1.0e-2  && abs(Cotes[4])>=1.0e-5) nc52_5=nc52_5+1;
if(abs(Cotes[4])<1.0e-5 && abs(Cotes[4])>=1.0e-10) nc55_10=nc55_10+1;
if(abs(Cotes[4])<1.0e-10 && abs(Cotes[4])>=1.0e-15) nc510_15=nc510_15+1;
if(abs(Cotes[4])<1.0e-15) nc515=nc515+1;
c5_sum=nc52+nc52_5+nc55_10+nc510_15+nc515;

if(abs(Cotes[5])>=1.0e-2 ) nc62=nc62+1;
if(abs(Cotes[5])<1.0e-2  && abs(Cotes[5])>=1.0e-5) nc62_5=nc62_5+1;
if(abs(Cotes[5])<1.0e-5 && abs(Cotes[5])>=1.0e-10) nc65_10=nc65_10+1;
if(abs(Cotes[5])<1.0e-10 && abs(Cotes[5])>=1.0e-15) nc610_15=nc610_15+1;
if(abs(Cotes[5])<1.0e-15) nc615=nc615+1;
c6_sum=nc62+nc62_5+nc65_10+nc610_15+nc615;

if(abs(Cotes[6])>=1.0e-2 ) nc72=nc72+1;
if(abs(Cotes[6])<1.0e-2  && abs(Cotes[6])>=1.0e-5) nc72_5=nc72_5+1;
if(abs(Cotes[6])<1.0e-5 && abs(Cotes[6])>=1.0e-10) nc75_10=nc75_10+1;
if(abs(Cotes[6])<1.0e-10 && abs(Cotes[6])>=1.0e-15) nc710_15=nc710_15+1;
if(abs(Cotes[6])<1.0e-15) nc715=nc715+1;
c7_sum=nc72+nc72_5+nc75_10+nc710_15+nc715;

if(abs(Cotes[7])>=1.0e-2 ) nc82=nc82+1;
if(abs(Cotes[7])<1.0e-2  && abs(Cotes[7])>=1.0e-5) nc82_5=nc82_5+1;
if(abs(Cotes[7])<1.0e-5 && abs(Cotes[7])>=1.0e-10) nc85_10=nc85_10+1;
if(abs(Cotes[7])<1.0e-10 && abs(Cotes[7])>=1.0e-15) nc810_15=nc810_15+1;
if(abs(Cotes[7])<1.0e-15) nc815=nc815+1;
c8_sum=nc82+nc82_5+nc85_10+nc810_15+nc815;

if(abs(Cotes[8])>=1.0e-2 ) nc92=nc92+1;
if(abs(Cotes[8])<1.0e-2  && abs(Cotes[8])>=1.0e-5) nc92_5=nc92_5+1;
if(abs(Cotes[8])<1.0e-5 && abs(Cotes[8])>=1.0e-10) nc95_10=nc95_10+1;
if(abs(Cotes[8])<1.0e-10 && abs(Cotes[8])>=1.0e-15) nc910_15=nc910_15+1;
if(abs(Cotes[8])<1.0e-15) nc915=nc915+1;
c9_sum=nc92+nc92_5+nc95_10+nc910_15+nc915;

if(abs(Cotes[9])>=1.0e-2 ) nc102=nc102+1;
if(abs(Cotes[9])<1.0e-2  && abs(Cotes[9])>=1.0e-5) nc102_5=nc102_5+1;
if(abs(Cotes[9])<1.0e-5 && abs(Cotes[9])>=1.0e-10) nc105_10=nc105_10+1;
if(abs(Cotes[9])<1.0e-10 && abs(Cotes[9])>=1.0e-15) nc1010_15=nc1010_15+1;
if(abs(Cotes[9])<1.0e-15) nc1015=nc1015+1;
c10_sum=nc102+nc102_5+nc105_10+nc1010_15+nc1015;


if(abs(Le2_ort)>=1.0e-2 ) nLe22=nLe22+1;
if(abs(Le2_ort)<1.0e-2  && abs(Le2_ort)>=1.0e-5) nLe22_5=nLe22_5+1;
if(abs(Le2_ort)<1.0e-5 && abs(Le2_ort)>=1.0e-10) nLe25_10=nLe25_10+1;
if(abs(Le2_ort)<1.0e-10 && abs(Le2_ort)>=1.0e-15) nLe210_15=nLe210_15+1;
if(abs(Le2_ort)<1.0e-15) nLe215=nLe215+1;
Le2_sum=nLe22+nLe22_5+nLe25_10+nLe210_15+nLe215;

if(abs(Le3_ort)>=1.0e-2 ) nLe32=nLe32+1;
if(abs(Le3_ort)<1.0e-2  && abs(Le3_ort)>=1.0e-5) nLe32_5=nLe32_5+1;
if(abs(Le3_ort)<1.0e-5 && abs(Le3_ort)>=1.0e-10) nLe35_10=nLe35_10+1;
if(abs(Le3_ort)<1.0e-10 && abs(Le3_ort)>=1.0e-15) nLe310_15=nLe310_15+1;
if(abs(Le3_ort)<1.0e-15) nLe315=nLe315+1;
Le3_sum=nLe32+nLe32_5+nLe35_10+nLe310_15+nLe315;

if(abs(Le4_ort)>=1.0e-2 ) nLe42=nLe42+1;
if(abs(Le4_ort)<1.0e-2  && abs(Le4_ort)>=1.0e-5) nLe42_5=nLe42_5+1;
if(abs(Le4_ort)<1.0e-5 && abs(Le4_ort)>=1.0e-10) nLe45_10=nLe45_10+1;
if(abs(Le4_ort)<1.0e-10 && abs(Le4_ort)>=1.0e-15) nLe410_15=nLe410_15+1;
if(abs(Le4_ort)<1.0e-15) nLe415=nLe415+1;
Le4_sum=nLe42+nLe42_5+nLe45_10+nLe410_15+nLe415;

if(abs(Le5_ort)>=1.0e-2 ) nLe52=nLe52+1;
if(abs(Le5_ort)<1.0e-2  && abs(Le5_ort)>=1.0e-5) nLe52_5=nLe52_5+1;
if(abs(Le5_ort)<1.0e-5 && abs(Le5_ort)>=1.0e-10) nLe55_10=nLe55_10+1;
if(abs(Le5_ort)<1.0e-10 && abs(Le5_ort)>=1.0e-15) nLe510_15=nLe510_15+1;
if(abs(Le5_ort)<1.0e-15) nLe515=nLe515+1;
Le5_sum=nLe52+nLe52_5+nLe55_10+nLe510_15+nLe515;

if(abs(Le6_ort)>=1.0e-2 ) nLe62=nLe62+1;
if(abs(Le6_ort)<1.0e-2  && abs(Le6_ort)>=1.0e-5) nLe62_5=nLe62_5+1;
if(abs(Le6_ort)<1.0e-5 && abs(Le6_ort)>=1.0e-10) nLe65_10=nLe65_10+1;
if(abs(Le6_ort)<1.0e-10 && abs(Le6_ort)>=1.0e-15) nLe610_15=nLe610_15+1;
if(abs(Le6_ort)<1.0e-15) nLe615=nLe615+1;
Le6_sum=nLe62+nLe62_5+nLe65_10+nLe610_15+nLe615;


if(abs(Ch2_ort)>=1.0e-2 ) nCh22=nCh22+1;
if(abs(Ch2_ort)<1.0e-2  && abs(Ch2_ort)>=1.0e-5) nCh22_5=nCh22_5+1;
if(abs(Ch2_ort)<1.0e-5 && abs(Ch2_ort)>=1.0e-10) nCh25_10=nCh25_10+1;
if(abs(Ch2_ort)<1.0e-10 && abs(Ch2_ort)>=1.0e-15) nCh210_15=nCh210_15+1;
if(abs(Ch2_ort)<1.0e-15) nCh215=nCh215+1;
Ch2_sum=nCh22+nCh22_5+nCh25_10+nCh210_15+nCh215;

if(abs(Ch3_ort)>=1.0e-2 ) nCh32=nCh32+1;
if(abs(Ch3_ort)<1.0e-2  && abs(Ch3_ort)>=1.0e-5) nCh32_5=nCh32_5+1;
if(abs(Ch3_ort)<1.0e-5 && abs(Ch3_ort)>=1.0e-10) nCh35_10=nCh35_10+1;
if(abs(Ch3_ort)<1.0e-10 && abs(Ch3_ort)>=1.0e-15) nCh310_15=nCh310_15+1;
if(abs(Ch3_ort)<1.0e-15) nCh315=nCh315+1;
Ch3_sum=nCh32+nCh32_5+nCh35_10+nCh310_15+nCh315;

if(abs(Ch4_ort)>=1.0e-2 ) nCh42=nCh42+1;
if(abs(Ch4_ort)<1.0e-2  && abs(Ch4_ort)>=1.0e-5)  nCh42_5=nCh42_5+1;
if(abs(Ch4_ort)<1.0e-5  && abs(Ch4_ort)>=1.0e-10) nCh45_10=nCh45_10+1;
if(abs(Ch4_ort)<1.0e-10 && abs(Ch4_ort)>=1.0e-15) nCh410_15=nCh410_15+1;
if(abs(Ch4_ort)<1.0e-15) nCh415=nCh415+1;
Ch4_sum=nCh42+nCh42_5+nCh45_10+nCh410_15+nCh415;

if(abs(Ch5_ort)>=1.0e-2 ) nCh52=nCh52+1;
if(abs(Ch5_ort)<1.0e-2  && abs(Ch5_ort)>=1.0e-5)  nCh52_5=nCh52_5+1;
if(abs(Ch5_ort)<1.0e-5  && abs(Ch5_ort)>=1.0e-10) nCh55_10=nCh55_10+1;
if(abs(Ch5_ort)<1.0e-10 && abs(Ch5_ort)>=1.0e-15) nCh510_15=nCh510_15+1;
if(abs(Ch5_ort)<1.0e-15) nCh515=nCh515+1;
Ch5_sum=nCh52+nCh52_5+nCh55_10+nCh510_15+nCh515;

if(abs(Ch6_ort)>=1.0e-2 ) nCh62=nCh62+1;
if(abs(Ch6_ort)<1.0e-2  && abs(Ch6_ort)>=1.0e-5)  nCh62_5=nCh62_5+1;
if(abs(Ch6_ort)<1.0e-5  && abs(Ch6_ort)>=1.0e-10) nCh65_10=nCh65_10+1;
if(abs(Ch6_ort)<1.0e-10 && abs(Ch6_ort)>=1.0e-15) nCh610_15=nCh610_15+1;
if(abs(Ch6_ort)<1.0e-15) nCh615=nCh615+1;
Ch6_sum=nCh62+nCh62_5+nCh65_10+nCh610_15+nCh615;
}

}//gx
out001<<"  "<<endl;
}//fx
out001.close();
out002<<"  "<<endl;
out002.close();

cout<<"div= "<<div<<endl;

out003<<"p_"<<"L"<<","<<div<<","
        <<tr_sum<<","<<ntr2<<","<<ntr2_5<<","<<ntr5_10<<","<<ntr10_15<<","<<ntr15<<","
        <<s3_sum<<","<<ns32<<","<<ns32_5<<","<<ns35_10<<","<<ns310_15<<","<<ns315<<","
        <<s8_sum<<","<<ns82<<","<<ns82_5<<","<<ns85_10<<","<<ns810_15<<","<<ns815<<","
        <<b4_sum<<","<<nb42<<","<<nb42_5<<","<<nb45_10<<","<<nb410_15<<","<<nb415<<","<<" "<<","

        <<tr_new_sum<<","<<ntr_new2<<","<<ntr_new2_5<<","<<ntr_new5_10<<","<<ntr_new10_15<<","<<ntr_new15<<","
        <<s3_new_sum<<","<<ns3_new2<<","<<ns3_new2_5<<","<<ns3_new5_10<<","<<ns3_new10_15<<","<<ns3_new15<<","
        <<s8_new_sum<<","<<ns8_new2<<","<<ns8_new2_5<<","<<ns8_new5_10<<","<<ns8_new10_15<<","<<ns8_new15<<","
        <<b4_new_sum<<","<<nb4_new2<<","<<nb4_new2_5<<","<<nb4_new5_10<<","<<nb4_new10_15<<","<<nb4_new15<<","<<" "<<","        

        <<c5_sum<<","<<nc52<<","<<nc52_5<<","<<nc55_10<<","<<nc510_15<<","<<nc515<<","
        <<c6_sum<<","<<nc62<<","<<nc62_5<<","<<nc65_10<<","<<nc610_15<<","<<nc615<<","
    <<c7_sum<<","<<nc72<<","<<nc72_5<<","<<nc75_10<<","<<nc710_15<<","<<nc715<<","
        <<c8_sum<<","<<nc82<<","<<nc82_5<<","<<nc85_10<<","<<nc810_15<<","<<nc815<<","
    <<c9_sum<<","<<nc92<<","<<nc92_5<<","<<nc95_10<<","<<nc910_15<<","<<nc915<<","
        <<c10_sum<<","<<nc102<<","<<nc102_5<<","<<nc105_10<<","<<nc1010_15<<","<<nc1015<<","<<" "<<","

        <<Le2_sum<<","<<nLe22<<","<<nLe22_5<<","<<nLe25_10<<","<<nLe210_15<<","<<nLe215<<","
        <<Le3_sum<<","<<nLe32<<","<<nLe32_5<<","<<nLe35_10<<","<<nLe310_15<<","<<nLe315<<","
        <<Le4_sum<<","<<nLe42<<","<<nLe42_5<<","<<nLe45_10<<","<<nLe410_15<<","<<nLe415<<","
        <<Le5_sum<<","<<nLe52<<","<<nLe52_5<<","<<nLe55_10<<","<<nLe510_15<<","<<nLe515<<","
        <<Le6_sum<<","<<nLe62<<","<<nLe62_5<<","<<nLe65_10<<","<<nLe610_15<<","<<nLe615<<","<<" "<<","
        
        <<Ch2_sum<<","<<nCh22<<","<<nCh22_5<<","<<nCh25_10<<","<<nCh210_15<<","<<nCh215<<","
        <<Ch3_sum<<","<<nCh32<<","<<nCh32_5<<","<<nCh35_10<<","<<nCh310_15<<","<<nCh315<<","
        <<Ch4_sum<<","<<nCh42<<","<<nCh42_5<<","<<nCh45_10<<","<<nCh410_15<<","<<nCh415<<","
        <<Ch5_sum<<","<<nCh52<<","<<nCh52_5<<","<<nCh55_10<<","<<nCh510_15<<","<<nCh515<<","
        <<Ch6_sum<<","<<nCh62<<","<<nCh62_5<<","<<nCh65_10<<","<<nCh610_15<<","<<nCh615<<","
        <<endl;

}// div0[i]
out003.close();



return 0;
}

vector<double> Legendre_function()
{
//Legendre関数p　
vector<double >p0(0+1,0.0);
p0[0]=1.0;

//以下　コード　L-1　に同じ



// 以上　L-1　に　同じ

p34[33]=0.0;
p34[34]=7113260368810144185/4294967296.0;


int k;
vector<double>hx;
k=0;for(int i=0;i<k+1;i++)      hx.push_back(p0[i]);
k=1;for(int i=0;i<k+1;i++)      hx.push_back(p1[i]);
// 以下　繰り返し　で削除 


// 以上　繰り返し　で　削除

k=34;for(int i=0;i<k+1;i++)     hx.push_back(p34[i]);
hx.resize(hx.size());

return hx;

}



vector<double>Newton_Cotes(int div,int j,int m,int n,double x_start, double x_end,
 vector<double>fx,vector<double>gx,vector<double>sum_ini)
{

double f_xn00=0.0;//分割始点
double f_xn10=0.0;//幅の1/10点

//以下 次章に記載する　あるいは　後日に追加する　ので削除


// 以上　次章に記載する　あるいは　後日に追加する　ので、削除

vector<double>Cotes_function(10,0.0);

Cotes_function[0]=tr_new;
Cotes_function[1]=s3_new;
Cotes_function[2]=s8_new;
Cotes_function[3]=b4_new;
Cotes_function[4]=c5_new;
Cotes_function[5]=c6_new;
Cotes_function[6]=c7_new;
Cotes_function[7]=c8_new;
Cotes_function[8]=c9_new;
Cotes_function[9]=c10_new;

return Cotes_function;

}


本章 7章の説明へ





3、Chebyshev多項式 (コード C-1)

#include <vector>
using namespace std;

const long double PI=3.14159265358979323846264338327950288; 

int main()
{
//Chebyshev関数
vector<long double >t0(0+1,0.0);
t0[0]=1.0;

vector<long double >t1(1+1,0.0);
t1[0]=0.0;
t1[1]=1.0;

vector<long double >t2(2+1,0.0);
t2[0]=-1.0;
t2[1]=0.0;
t2[2]=2.0;

vector<long double >t3(3+1,0.0);
t3[0]=0.0;
t3[1]=-3.0;
t3[2]=0.0;
t3[3]=4.0;

vector<long double >t4(4+1,0.0);
t4[0]=1.0;
t4[1]=0.0;
t4[2]=-8.0;
t4[3]=0.0;
t4[4]=8.0;

vector<long double >t5(5+1,0.0);
t5[0]=0.0;
t5[1]=5.0;
t5[2]=0.0;
t5[3]=-20.0;
t5[4]=0.0;
t5[5]=16.0;

vector<long double >t6(6+1,0.0);
t6[0]=-1.0;
t6[1]=0.0;
t6[2]=18.0;
t6[3]=0.0;
t6[4]=-48.0;
t6[5]=0.0;
t6[6]=32.0;     

vector<long double>t7(7+1,0.0);
t7[0]=0.0;
t7[1]=-7.0;
t7[2]=0.0;
t7[3]=56.0;
t7[4]=0.0;
t7[5]=-112.0;
t7[6]=0.0;
t7[7]=64.0;

vector<long double>t8(8+1,0.0);
t8[0]=1.0;
t8[1]=0.0;
t8[2]=-32.0;
t8[3]=0.0;
t8[4]=160.0;
t8[5]=0.0;
t8[6]=-256.0;
t8[7]=0.0;
t8[8]=128.0;

vector<long double>t9(9+1,0.0);
t9[0]=0.0;
t9[1]=9.0;
t9[2]=0.0;
t9[3]=-120.0;
t9[4]=0.0;
t9[5]=432.0;
t9[6]=0.0;
t9[7]=-576.0;
t9[8]=0.0;
t9[9]=256.0;

vector<long double>t10(10+1,0.0);
t10[0]=-1.0;
t10[1]=0.0;
t10[2]=50.0;
t10[3]=0.0;
t10[4]=-400;
t10[5]=0.0;
t10[6]=1120.0;
t10[7]=0.0;
t10[8]=-1280.0;
t10[9]=0.0;
t10[10]=512.0;

vector<long double>t11(11+1,0.0);
t11[0]=0.0;
t11[1]=-11.0;
t11[2]=0.0;
t11[3]=220.0;
t11[4]=0.0;
t11[5]=-1232;
t11[6]=0.0;
t11[7]=2816.0;// need check 
t11[8]=0.0;
t11[9]=-2816.0;
t11[10]=0.0;
t11[11]=1024.0;

vector<long double>t12(12+1,0.0);
t12[0]=1.0;
t12[1]=0.0;
t12[2]=-72.0;
t12[3]=0.0;
t12[4]=840.0;
t12[5]=0.0;
t12[6]=-3584.0;
t12[7]=0.0;
t12[8]=6912.0;
t12[9]=0.0;
t12[10]=-6144.0;
t12[11]=0.0;
t12[12]=2048.0;

vector<long double>t13(13+1,0.0);
t13[0]=0.0;
t13[1]=13.0;
t13[2]=0.0;
t13[3]=-364.0;
t13[4]=0.0;
t13[5]=2912.0;
t13[6]=0.0;
t13[7]=-9984.0;
t13[8]=0.0;
t13[9]=16640.0;
t13[10]=0.0;
t13[11]=-13312.0;
t13[12]=0.0;
t13[13]=4096.0;


vector<long double>t14(14+1,0.0);
t14[0]=-1.0;
t14[1]=0.0;
t14[2]=98.0;
t14[3]=0.0;
t14[4]=-1568.0;
t14[5]=0.0;
t14[6]=9408.0;
t14[7]=0.0;
t14[8]=-26880.0;
t14[9]=0.0;
t14[10]=39424.0;
t14[11]=0.0;
t14[12]=-28672.0;
t14[13]=0.0;
t14[14]=8192.0;

vector<long double>t15(15+1,0.0);
t15[0]=0.0;
t15[1]=-15.0;
t15[2]=0.0;
t15[3]=560.0;
t15[4]=0.0;
t15[5]=-6048.0;
t15[6]=0.0;
t15[7]=28800.0;
t15[8]=0.0;
t15[9]=-70400.0;
t15[10]=0.0;
t15[11]=92160.0;
t15[12]=0.0;
t15[13]=-61440.0;
t15[14]=0.0;
t15[15]=16384.0;

vector<long double>t16(16+1,0.0);
t16[0]=1.0;
t16[1]=0.0;
t16[2]=-128.0;
t16[3]=0.0;
t16[4]=2688.0;
t16[5]=0.0;
t16[6]=-21504.0;
t16[7]=00.0;
t16[8]=84480.0;
t16[9]=0.0;
t16[10]=-180224.0;
t16[11]=0.0;
t16[12]=212992.0;
t16[13]=00.0;
t16[14]=-131072.0;
t16[15]=0.0;
t16[16]=32768.0;

vector<long double>t17(17+1,0.0);
t17[0]= 0.0;
t17[1]=17.0;
t17[2]=0.0;
t17[3]=-816.0;
t17[4]= 0.0;
t17[5]=11424.0;
t17[6]= 0.0;
t17[7]=-71808.0;
t17[8]= 0.0;
t17[9]=239360.0;
t17[10]=0.0;
t17[11]=-452608.0;
t17[12]=0.0;
t17[13]=487424.0;
t17[14]=0.0;
t17[15]=-278528.0;
t17[16]=0.0;
t17[17]=65536.0;

vector<long double>t18(18+1,0.0);
t18[0]=-1.0;
t18[1]=0.0;
t18[2]=162.0;
t18[3]=0.0;
t18[4]=-4320.0;
t18[5]=0.0;
t18[6]=44352.0;
t18[7]=0.0;
t18[8]=-228096.0;
t18[9]=0.0;
t18[10]=658944.0;
t18[11]=0.0;
t18[12]=-1118208.0;
t18[13]=0.0;
t18[14]=1105920.0;
t18[15]=0.0;
t18[16]=-589824.0;
t18[17]=0.0;
t18[18]=131072.0;

vector<long double>t19(19+1,0.0);
t19[0]=0.0;             
t19[1]=-19.0;
t19[2]=0.0;             
t19[3]=1140.0;
t19[4]=0.0;             
t19[5]=-20064.0;
t19[6]=0.0;             
t19[7]=160512.0;
t19[8]=0.0;             
t19[9]=-695552.0;
t19[10]=0.0;            
t19[11]=1770496.0;
t19[12]=0.0;            
t19[13]=-2723840.0;
t19[14]=0.0;            
t19[15]=2490368.0;
t19[16]=0.0;            
t19[17]=-1245184.0;
t19[18]=0.0;            
t19[19]=262144.0;


vector<long double>t20(20+1,0.0);
t20[0]=1.0;
t20[1]=0.0;             
t20[2]=-200.0;
t20[3]=0.0;             
t20[4]=6600.0;
t20[5]=0.0;             
t20[6]=-84480.0;
t20[7]=0.0;             
t20[8]=549120.0;
t20[9]=0.0;             
t20[10]=-2050048.0;
t20[11]=0.0;            
t20[12]=4659200.0;
t20[13]=0.0;            
t20[14]=-6553600.0;
t20[15]=0.0;            
t20[16]=5570560.0;
t20[17]=0.0;            
t20[18]=-2621440.0;
t20[19]=0.0;            
t20[20]=524288.0;

vector<long double>t21(21+1,0.0);
t21[0]=0.0;             
t21[1]=21.0;
t21[2]=0.0;             
t21[3]=-1540.0;
t21[4]=0.0;             
t21[5]=33264.0;
t21[6]=0.0;             
t21[7]=-329472.0;
t21[8]=0.0;             
t21[9]=1793792.0;
t21[10]=0.0;            
t21[11]=-5870592.0;
t21[12]=0.0;            
t21[13]=12042240.0;
t21[14]=0.0;            
t21[15]=-15597568.0;
t21[16]=0.0;            
t21[17]=12386304.0;
t21[18]=0.0;            
t21[19]=-5505024.0;
t21[20]=0.0;            
t21[21]=1048576.0;

vector<long double>t22(22+1,0.0);
t22[0]=-1.0;
t22[1]=0.0;             
t22[2]=242.0;
t22[3]=0.0;             
t22[4]=-9680.0;
t22[5]=0.0;             
t22[6]=151008.0;
t22[7]=0.0;             
t22[8]=-1208064.0;
t22[9]=0.0;             
t22[10]=5637632.0;
t22[11]=0.0;            
t22[12]=-16400384.0;
t22[13]=0.0;            
t22[14]=30638080.0;
t22[15]=0.0;            
t22[16]=-36765696.0;
t22[17]=0.0;            
t22[18]=27394048.0;
t22[19]=0.0;            
t22[20]=-11534336.0;
t22[21]=0.0;            
t22[22]=2097152.0;

vector<long double>t23(23+1,0.0);
t23[0]=0.0;             
t23[1]=-23.0;
t23[2]=0.0;             
t23[3]=2024.0;
t23[4]=0.0;             
t23[5]=-52624.0;
t23[6]=0.0;             
t23[7]=631488.0;
t23[8]=0.0;             
t23[9]=-4209920.0;
t23[10]=0.0;            
t23[11]=17145856.0;
t23[12]=0.0;            
t23[13]=-44843008.0;
t23[14]=0.0;            
t23[15]=76873728.0;
t23[16]=0.0;            
t23[17]=-85917696.0;
t23[18]=0.0;            
t23[19]=60293120.0;
t23[20]=0.0;            
t23[21]=-24117248.0;
t23[22]=0.0;            
t23[23]=4194304.0;

vector<long double>t24(24+1,0.0);
t24[0]=1.0;
t24[1]=0.0;             
t24[2]=-288.0;
t24[3]=0.0;             
t24[4]=13728.0;
t24[5]=0.0;             
t24[6]=-256256.0;
t24[7]=0.0;             
t24[8]=2471040.0;
t24[9]=0.0;             
t24[10]=-14057472.0;
t24[11]=0.0;            
t24[12]=50692096.0;
t24[13]=0.0;            
t24[14]=-120324096.0;
t24[15]=0.0;            
t24[16]=190513152.0;
t24[17]=0.0;            
t24[18]=-199229440.0;
t24[19]=0.0;            
t24[20]=132120576.0;
t24[21]=0.0;            
t24[22]=-50331648.0;
t24[23]=0.0;            
t24[24]=8388608.0;

vector<long double>t25(25+1,0.0);
t25[0]=0.0;             
t25[1]=25.0;
t25[2]=0.0;             
t25[3]=-2600.0;
t25[4]=0.0;             
t25[5]=80080.0;
t25[6]=0.0;             
t25[7]=-1144000.0;
t25[8]=0.0;             
t25[9]=9152000.0;
t25[10]=0.0;            
t25[11]=-45260800.0;
t25[12]=0.0;            
t25[13]=146227200.0;
t25[14]=0.0;            
t25[15]=-317521920.0;
t25[16]=0.0;            
t25[17]=466944000.0;
t25[18]=0.0;            
t25[19]=-458752000.0;
t25[20]=0.0;            
t25[21]=288358400.0;
t25[22]=0.0;            
t25[23]=-104857600.0;
t25[24]=0.0;            
t25[25]=16777216.0;

vector<long double>t26(26+1,0.0);
t26[0]=-1.0;
t26[1]=0.0;
t26[2]=338.0;
t26[3]=0.0;
t26[4]=-18928.0;
t26[5]=0.0;
t26[6]=416416.0;
t26[7]=0.0;
t26[8]=-4759040.0;
t26[9]=0.0;
t26[10]=32361472.0;
t26[11]=0.0;
t26[12]=-141213696.0;
t26[13]=0.0;
t26[14]=412778496.0;
t26[15]=0.0;
t26[16]=-825556992.0;
t26[17]=0.0;
t26[18]=1133117440.0;
t26[19]=0.0;
t26[20]=-1049624576.0;
t26[21]=0.0;
t26[22]=627048448.0;
t26[23]=0.0;
t26[24]=-218103808.0;
t26[25]=0.0;
t26[26]=33554432.0;

vector<long double>t27(27+1,0.0);
t27[0]=0.0;
t27[1]=-27.0;
t27[2]=0.0;
t27[3]=3276.0;
t27[4]=0.0;
t27[5]=-117936.0;
t27[6]=0.0;
t27[7]=1976832.0;
t27[8]=0.0;
t27[9]=-18670080.0;
t27[10]=0.0;
t27[11]=109983744.0;
t27[12]=0.0;
t27[13]=-428654592.0;
t27[14]=0.0;
t27[15]=1143078912.0;
t27[16]=0.0;
t27[17]=-2118057984.0;
t27[18]=0.0;
t27[19]=2724986880.0;
t27[20]=0.0;
t27[21]=-2387607552.0;
t27[22]=0.0;
t27[23]=1358954496.0;
t27[24]=0.0;
t27[25]=-452984832.0;
t27[26]=0.0;
t27[27]=67108864.0; 

vector<long double>t28(28+1,0.0);
t28[0]=1.0;
t28[1]=0.0;
t28[2]=-392.0;
t28[3]=0.0;
t28[4]=25480.0;
t28[5]=0.0;
t28[6]=-652288.0;
t28[7]=0.0;
t28[8]=8712704.0;
t28[9]=0.0;
t28[10]=-69701632.0;
t28[11]=0.0;
t28[12]=361181184.0;
t28[13]=0.0;
t28[14]=-1270087680.0;
t28[15]=0.0;
t28[16]=3111714816.0;
t28[17]=0.0;
t28[18]=-5369233408.0;
t28[19]=0.0;
t28[20]=6499598336.0;
t28[21]=0.0;
t28[22]=-5402263552.0;
t28[23]=0.0;
t28[24]=2936012800.0;
t28[25]=0.0;
t28[26]=-939524096.0;
t28[27]=0.0;
t28[28]=134217728.0;

vector<long double>t29(29+1,0.0);
t29[0]=0.0;
t29[1]=29.0;
t29[2]=0.0;
t29[3]=-4060.0;
t29[4]=0.0;
t29[5]=168896.0;
t29[6]=0.0;
t29[7]=-3281408.0;
t29[8]=0.0;
t29[9]=36095488.0;
t29[10]=0.0;
t29[11]=-249387008.0;
t29[12]=0.0;
t29[13]=1151016960.0;
t29[14]=0.0;
t29[15]=-3683254272.0;
t29[16]=0.0;
t29[17]=8341487616.0;
t29[18]=0.0;
t29[19]=-13463453696.0;
t29[20]=0.0;
t29[21]=15386804224.0;
t29[22]=0.0;
t29[23]=-12163481600.0;
t29[24]=0.0;
t29[25]=6325010432.0;
t29[26]=0.0;
t29[27]=-1946157056.0;
t29[28]=0.0;
t29[29]=268435456.0;

vector<long double>t30(30+1,0.0);
t30[0]=-1.0;
t30[1]=0.0;
t30[2]=450.0;
t30[3]=0.0;
t30[4]=-33600.0;
t30[5]=0.0;
t30[6]=990080.0;
t30[7]=0.0;
t30[8]=-15275520.0;
t30[9]=0.0;
t30[10]=141892608.0;
t30[11]=0.0;
t30[12]=-859955200.0;
t30[13]=0.0;
t30[14]=3572121600.0;
t30[15]=0.0;
t30[16]=-10478223360.0;
t30[17]=0.0;
t30[18]=22052208640.0;
t30[19]=0.0;
t30[20]=-33426505728.0;
t30[21]=0.0;
t30[22]=36175872000.0;
t30[23]=0.0;
t30[24]=-27262976000.0;
t30[25]=0.0;
t30[26]=13589544960.0;
t30[27]=0.0;
t30[28]=-4026531840.0;
t30[29]=0.0;
t30[30]=536870912.0;

vector<long double>t31(31+1,0.0);
t31[0]=0.0;
t31[1]=-31.0;
t31[2]=0.0;
t31[3]=4960.0;
t31[4]=0.0;
t31[5]=-236096.0;
t31[6]=0.0;
t31[7]=5261568.0;
t31[8]=0.0;
t31[9]=-66646528.0;
t31[10]=0.0;
t31[11]=533172224.0;
t31[12]=0.0;
t31[13]=-2870927360.0;
t31[14]=0.0;
t31[15]=10827497472.0;
t31[16]=0.0;
t31[17]=-29297934336.0;
t31[18]=0.0;
t31[19]=57567870976.0;
t31[20]=0.0;
t31[21]=-82239815680.0;
t31[22]=0.0;
t31[23]=84515225600.0;
t31[24]=0.0;
t31[25]=-60850962432.0;
t31[26]=0.0;
t31[27]=29125246976.0;
t31[28]=0.0;
t31[29]=-8321499136.0;
t31[30]=0.0;
t31[31]=1073741824.0;

vector<long double>t32(32+1,0.0);
t32[0]=1.0;
t32[1]=0.0;
t32[2]=-512.0;
t32[3]=0.0;
t32[4]=43520.0;
t32[5]=0.0;
t32[6]=-1462272.0;
t32[7]=0.0;
t32[8]=25798656.0;
t32[9]=0.0;
t32[10]=-275185664.0;
t32[11]=0.0;
t32[12]=1926299648.0;
t32[13]=0.0;
t32[14]=-9313976320.0;
t32[15]=0.0;
t32[16]=32133218304.0;
t32[17]=0.0;
t32[18]=-80648077312.0;
t32[19]=0.0;
t32[20]=148562247680.0;
t32[21]=0.0;
t32[22]=-200655503360.0;
t32[23]=0.0;
t32[24]=196293427200.0;
t32[25]=0.0;
t32[26]=-135291469824.0;
t32[27]=0.0;
t32[28]=62277025792.0;
t32[29]=0.0;
t32[30]=-17179869184.0;
t32[31]=0.0;
t32[32]=2147483648.0;

vector<long double>t33(33+1,0.0);
t33[0]=0.0;
t33[1]=33.0;
t33[2]=0.0;
t33[3]=-5984.0;
t33[4]=0.0;
t33[5]=323136.0;
t33[6]=0.0;
t33[7]=-8186112.0;
t33[8]=0.0;
t33[9]=118243840.0;
t33[10]=0.0;
t33[11]=-1083543552.0;
t33[12]=0.0;
t33[13]=6723526656.0;
t33[14]=0.0;
t33[15]=-29455450112.0;
t33[16]=0.0;
t33[17]=93564370944.0;
t33[18]=0.0;
t33[19]=-218864025600.0;
t33[20]=0.0;
t33[21]=379364311040.0;
t33[22]=0.0;
t33[23]=-485826232320.0;
t33[24]=0.0;
t33[25]=453437816832.0;
t33[26]=0.0;
t33[27]=-299708186624.0;
t33[28]=0.0;
t33[29]=132875550720.0;
t33[30]=0.0;
t33[31]=-35433480192.0;
t33[32]=0.0;
t33[33]=4294967296.0;

vector<long double>t34(34+1,0.0);
t34[0]=-1.0;
t34[1]=0.0;
t34[2]=578.0;
t34[3]=0.0;
t34[4]=-55488.0;
t34[5]=0.0;
t34[6]=2108544.0;
t34[7]=0.0;
t34[8]=-42170880.0;
t34[9]=0.0;
t34[10]=511673344.0;
t34[11]=0.0;
t34[12]=-4093386752.0;
t34[13]=0.0;
t34[14]=22761029632.0;
t34[15]=0.0;
t34[16]=-91044118528.0;
t34[17]=0.0;
t34[18]=267776819200.0;
t34[19]=0.0;
t34[20]=-586290298880.0;
t34[21]=0.0;
t34[22]=959384125440.0;
t34[23]=0.0;
t34[24]=-1167945891840.0;
t34[25]=0.0;
t34[26]=1042167103488.0;
t34[27]=0.0;
t34[28]=-661693399040.0;
t34[29]=0.0;
t34[30]=282930970624.0;
t34[31]=0.0;
t34[32]=-73014444032.0;
t34[33]=0.0;
t34[34]=8589934592.0; 

vector<long double>t35(35+1,0.0);
t35[0]=0.0;
t35[1]=-35.0;
t35[2]=0.0;
t35[3]=7140.0;
t35[4]=0.0;
t35[5]=-434112.0;
t35[6]=0.0;
t35[7]=12403200.0;
t35[8]=0.0;
t35[9]=-202585600.0;
t35[10]=0.0;
t35[11]=2106890240.0;
t35[12]=0.0;
t35[13]=-14910300160.0;
t35[14]=0.0;
t35[15]=74977509376.0;
t35[16]=0.0;
t35[17]=-275652608000.0;
t35[18]=0.0;
t35[19]=754417664000.0;
t35[20]=0.0;
t35[21]=-1551944908800.0;
t35[22]=0.0;
t35[23]=2404594483200.0;
t35[24]=0.0;
t35[25]=-2789329600512.0;
t35[26]=0.0;
t35[27]=2384042393600.0;
t35[28]=0.0;
t35[29]=-1456262348800.0;
t35[30]=0.0;
t35[31]=601295421440.0;
t35[32]=0.0;
t35[33]=-150323855360.0;
t35[34]=0.0;
t35[35]=17179869184.0;

return 0;
}


本章 7章の説明へ



4、Chebyshev 多項式の直交性確認 ( コード C-2 )
#include <cmath>
#include <fstream>
#include <vector>
#include <iomanip>
#include <numeric>
#include <iostream>
#include <string>
#include <sstream>
using namespace std;

#include <direct.h>// for getcwd
const int BUFFSIZE=1000;

const long double PI=3.14159265358979323846264338327950288; 

vector<double> Chebyshev_function();
vector<double>Newton_Cotes(int div,int j,int m,int n,double x0,       
double x1,vector<double>fx,vector<double>gx,vector<double>sum_ini);

int main()
{

//Gauss-Legendre
//2分点
double x20=-1.0/sqrt(3.0);
double x21=1.0/sqrt(3.0);

//重み係数
double wLe2_0=1.0;
double wLe2_1=1.0;
double Le2_0=0.0,Le2_1=0.0;
for(int i=0;i<m+1;i++) 
 { 
  Le2_0=Le2_0+fx[i]*pow(cos(xLe2_0),i);
  Le2_1=Le2_1+fx[i]*pow(cos(xLe2_1),i); 
 }

double gLe2_0=0.0,gLe2_1=0.0;
for(int i=0;i<n+1;i++) 
 { 
  gLe2_0=gLe2_0+gx[i]*pow(cos(xLe2_0),i);
  gLe2_1=gLe2_1+gx[i]*pow(cos(xLe2_1),i); 
 }

Le2_ort=Le2_ort+h/2.0*(wLe2_0*Le2_0*gLe2_0+wLe2_1*Le2_1*gLe2_1);

// 以下　次章に記載する　あるいは後日に記載する　ので　削除 



// 以上　次章に記載する　あるいは　後日に追加sする　ので　削除

double xCh65=0.86624681810782;
double wCh6=1.0/3.0;

//計算する分割数
vector<int>div0(20+1,0);

div0[0]=1;
div0[1]=2;
div0[2]=4;
div0[3]=5;
div0[4]=7;

div0[5]=10;
div0[6]=16;
div0[7]=25;
div0[8]=40;
div0[9]=63;

div0[10]=100;
div0[11]=160;

div0[12]=250;
div0[13]=400;
div0[14]=630;

div0[15]=1000;
div0[16]=1600;
div0[17]=2500;
div0[18]=4000;
div0[19]=6300;

//非対角要素の分割数による精度確認 
char dirdata3[BUFFSIZE]; 
_getcwd(dirdata3,BUFFSIZE);
string file_name3="\\accracy_distribution_ChebyshevTXX_YY.csv";
strcat_s(dirdata3,file_name3.c_str());

fstream out003(dirdata3,ios::out|ios::binary|ios::app);

out003<<"p_"<<"L"<<","<<"div"<<","
        <<"tr_sum"<<","<<"tr more1.0e-2"<<","<<"tr 1.0e-2_1.0e-5"<<","<<"tr 1.0e-5_1.0e-10"<<"," 
<<"tr 1.0e-10_1.0e-15"<<","<<"tr less than 1.0e-15"<<","
        <<"s3_sum"<<","<<"s3 more1.0e-2"<<","<<"s3 1.0e-2_1.0e-5"<<","<<"s3 1.0e-5_1.0e-10"<<","
<<"s3 1.0e-10_1.0e-15"<<","<<"s3 less than 1.0e-15"<<","
        <<"s8_sum"<<","<<"s8 more1.0e-2"<<","<<"s8 1.0e-2_1.0e-5"<<","<<"s8 1.0e-5_1.0e-10"<<","
<<"s8 1.0e-10_1.0e-15"<<","<<"s8 less than 1.0e-15"<<","
        <<"b4_sum"<<","<<"b4 more1.0e-2"<<","<<"b4 1.0e-2_1.0e-5"<<","<<"b4 1.0e-5_1.0e-10"<<","
<<"b4 1.0e-10_1.0e-15"<<","<<"b4 less than 1.0e-15"<<","<<" "<<","

        
        <<"tr_new_sum"<<","<<"tr_new more1.0e-2"<<","<<"tr_new 1.0e-2_1.0e-5"<<","<<"tr_new 1.0e-5_1.0e-10"           
<<","<<"tr_new 1.0e-10_1.0e-15"<<","<<"tr_new less than 1.0e-15"<<","
        <<"s3_new_sum"<<","<<"s3_new more1.0e-2"<<","<<"s3_new 1.0e-2_1.0e-5"<<","<<"s3_new 1.0e-5_1.0e-10"
<<","<<"s3_new 1.0e-10_1.0e-15"<<","<<"s3_new less than 1.0e-15"<<","
        <<"s8_new_sum"<<","<<"s8_new more1.0e-2"<<","<<"s8_new 1.0e-2_1.0e-5"<<","<<"s8_new 1.0e-5_1.0e-10"
<<","<<"s8_new 1.0e-10_1.0e-15"<<","<<"s8_new less than 1.0e-15"<<","
        <<"b4_new_sum"<<","<<"b4_new more1.0e-2"<<","<<"b4_new 1.0e-2_1.0e-5"<<","<<"b4_new 1.0e-5_1.0e-10"
<<","<<"b4_new 1.0e-10_1.0e-15"<<","<<"b4_new less than 1.0e-15"<<","<<" "<<","      

        <<"c5_sum"<<","<<"c5 more1.0e-2"<<","<<"c5 1.0e-2_1.0e-5"<<","<<"c5 1.0e-5_1.0e-10"<<","
<<"c5 1.0e-10_1.0e-15"<<","<<"c5 less than 1.0e-15"<<","
        <<"c6_sum"<<","<<"c6 more1.0e-2"<<","<<"c6 1.0e-2_1.0e-5"<<","<<"c6 1.0e-5_1.0e-10"<<","
<<"c6 1.0e-10_1.0e-15"<<","<<"c6 less than 1.0e-15"<<","
        <<"c7_sum"<<","<<"c7 more1.0e-2"<<","<<"c7 1.0e-2_1.0e-5"<<","<<"c7 1.0e-5_1.0e-10"<<","
<<"c7 1.0e-10_1.0e-15"<<","<<"c7 less than 1.0e-15"<<","
        <<"c8_sum"<<","<<"c8 more1.0e-2"<<","<<"c8 1.0e-2_1.0e-5"<<","<<"c8 1.0e-5_1.0e-10"<<","
<<"c8 1.0e-10_1.0e-15"<<","<<"c8 less than 1.0e-15"<<","        
        <<"c9_sum"<<","<<"c9 more1.0e-2"<<","<<"c9 1.0e-2_1.0e-5"<<","<<"c9 1.0e-5_1.0e-10"<<","
<<"c9 1.0e-10_1.0e-15"<<","<<"c9 less than 1.0e-15"<<","
        <<"c10_sum"<<","<<"c10 more1.0e-2"<<","<<"c10 1.0e-2_1.0e-5"<<","<<"c10 1.0e-5_1.0e-10"<<","
<<"c10 1.0e-10_1.0e-15"<<","<<"c10 less than 1.0e-15"<<","<<" "<<","


        <<"Le2_sum"<<","<<"Le2 more1.0e-2"<<","<<"Le2 1.0e-2_1.0e-5"<<","<<"Le2 1.0e-5_1.0e-10"<<","
<<"Le2 1.0e-10_1.0e-15"<<","<<"Le2 less than 1.0e-15"<<","
        <<"Le3_sum"<<","<<"Le3 more1.0e-2"<<","<<"Le3 1.0e-2_1.0e-5"<<","<<"Le3 1.0e-5_1.0e-10"<<","
<<"Le3 1.0e-10_1.0e-15"<<","<<"Le3 less than 1.0e-15"<<","
        <<"Le4_sum"<<","<<"Le4 more1.0e-2"<<","<<"Le4 1.0e-2_1.0e-5"<<","<<"Le4 1.0e-5_1.0e-10"<<","
<<"Le4 1.0e-10_1.0e-15"<<","<<"Le4 less than 1.0e-15"<<","
        <<"Le5_sum"<<","<<"Le5 more1.0e-2"<<","<<"Le5 1.0e-2_1.0e-5"<<","<<"Le5 1.0e-5_1.0e-10"<<","
<<"Le5 1.0e-10_1.0e-15"<<","<<"Le5 less than 1.0e-15"<<","
        <<"Le6_sum"<<","<<"Le6 more1.0e-2"<<","<<"Le6 1.0e-2_1.0e-5"<<","<<"Le6 1.0e-5_1.0e-10"<<","
<<"Le6 1.0e-10_1.0e-15"<<","<<"Le6 less than 1.0e-15"<<","<<" "<<","
        
        <<"Ch2_sum"<<","<<"Ch2 more1.0e-2"<<","<<"Ch2 1.0e-2_1.0e-5"<<","<<"Ch2 1.0e-5_1.0e-10"<<","
<<"Ch2 1.0e-10_1.0e-15"<<","<<"Ch2 less than 1.0e-15"<<","
        <<"Ch3_sum"<<","<<"Ch3 more1.0e-2"<<","<<"Ch3 1.0e-2_1.0e-5"<<","<<"Ch3 1.0e-5_1.0e-10"<<","
<<"Ch3 1.0e-10_1.0e-15"<<","<<"Ch3 less than 1.0e-15"<<","
        <<"Ch4_sum"<<","<<"Ch4 more1.0e-2"<<","<<"Ch4 1.0e-2_1.0e-5"<<","<<"Ch4 1.0e-5_1.0e-10"<<","
<<"Ch4 1.0e-10_1.0e-15"<<","<<"Ch4 less than 1.0e-15"<<","
        <<"Ch5_sum"<<","<<"Ch5 more1.0e-2"<<","<<"Ch5 1.0e-2_1.0e-5"<<","<<"Ch5 1.0e-5_1.0e-10"<<","
<<"Ch5 1.0e-10_1.0e-15"<<","<<"Ch5 less than 1.0e-15"<<","
        <<"Ch6_sum"<<","<<"Ch6 more1.0e-2"<<","<<"Ch6 1.0e-2_1.0e-5"<<","<<"Ch6 1.0e-5_1.0e-10"<<","
<<"Ch6 1.0e-10_1.0e-15"<<","<<"Ch6 less than 1.0e-15"<<","<<" "<<","
        <<endl;
        

double x0=0.0;
double x1=PI; 


for(int i=0;i<(int)div0.size();i++)
{
//分割数毎にcsv形式のfile出力を行う準備
stringstream division;
division <<div0[i];
string str = division.str();


char dirdata1[BUFFSIZE]; 
_getcwd(dirdata1,BUFFSIZE);// <direct.h>が必要
string file_end="_div_ChebyshevTXX_YY.csv";
string file_name="\\"+str+file_end;
strcat_s(dirdata1,file_name.c_str());//ファイル名のdirを生成

fstream out001(dirdata1,ios::out | ios::binary |ios::app);
out001<<"p_"<<"XX"<<"_"<<"YY"<<","<<"div"<<","
        <<"tr_ort/analytic"<<","<<"s3_ort/analytic"<<","<<"s8_ort/analytic"<<","<<"b4_ort/analytic"<<","<<" "<<","
        <<"tr_new/analytic"<<","<<"s3_new/analytic"<<","<<"s8_new/analytic"<<","<<"b4_new/analytic"<<","<<" "<<","
        <<"c5_new/analytic"<<","<<"c6_new/analytic"<<","<<"c7_new/analytic"<<","<<"c8_new/analytic"<<","
<<"c9_new/analytic"<<","<<"c10_new/analytic"<<","<<" "<<","
        <<"Le2_ort/analytic"<<","<<"Le3_ort/analytic"<<","<<"Le4_ort/analytic"<<","<<"Le5_ort/analytic"
<<","<<"Le6_ort/analytic"<<","<<" "<<","
        <<"Ch2_ort/analytic"<<","<<"Ch3_ort/analytic"<<","<<"Ch4_ort/analytic"<<","<<"Ch5_ort/analytic"
<<","<<"Ch6_ort/analytic"<<","<<" "<<","
        <<"analytic_value"<<endl;


char dirdata2[BUFFSIZE]; 
_getcwd(dirdata2,BUFFSIZE);
string file_end2="_div_ChebyshevTXX_XX.csv";
string file_name2="\\"+str+file_end2;
strcat_s(dirdata2,file_name2.c_str());
fstream out002(dirdata2,ios::out | ios::binary |ios::app);
out002<<"p_"<<"XX"<<"_"<<"XX"<<","<<"div"<<","
        <<"tr_ort/analytic"<<","<<"s3_ort/analytic"<<","<<"s8_ort/analytic"<<","<<"b4_ort/analytic"<<","<<" "<<","
        <<"tr_new/analytic"<<","<<"s3_new/analytic"<<","<<"s8_new/analytic"<<","<<"b4_new/analytic"<<","<<" "<<","
        <<"c5_new/analytic"<<","<<"c6_new/analytic"<<","<<"c7_new/analytic"<<","<<"c8_new/analytic"<<","
<<"c9_new/analytic"<<","<<"c10_new/analytic"<<","<<" "<<","
        <<"Le2_ort/analytic"<<","<<"Le3_ort/analytic"<<","<<"Le4_ort/analytic"<<","<<"Le5_ort/analytic"<<","
<<"Le6_ort/analytic"<<","<<" "<<","
        <<"Ch2_ort/analytic"<<","<<"Ch3_ort/analytic"<<","<<"Ch4_ort/analytic"<<","<<"Ch5_ort/analytic"<<","
<<"Ch6_ort/analytic"<<","<<" "<<","
        <<"analytic_value"<<endl;

//計算結果の精度範囲の個数カウントの初期化 
int ntr2=0;
int ntr2_5=0;
int ntr5_10=0;
int ntr10_15=0;
int ntr15=0;

int ns32=0;
int ns32_5=0;
int ns35_10=0;
int ns310_15=0;
int ns315=0;

int ns82=0;
int ns82_5=0;
int ns85_10=0;
int ns810_15=0;
int ns815=0;

int nb42=0;
int nb42_5=0;
int nb45_10=0;
int nb410_15=0;
int nb415=0;


int ntr_new2=0;
int ntr_new2_5=0;
int ntr_new5_10=0;
int ntr_new10_15=0;
int ntr_new15=0;

int ns3_new2=0;
int ns3_new2_5=0;
int ns3_new5_10=0;
int ns3_new10_15=0;
int ns3_new15=0;

int ns8_new2=0;
int ns8_new2_5=0;
int ns8_new5_10=0;
int ns8_new10_15=0;
int ns8_new15=0;

int nb4_new2=0;
int nb4_new2_5=0;
int nb4_new5_10=0;
int nb4_new10_15=0;
int nb4_new15=0;


int nc52=0;
int nc52_5=0;
int nc55_10=0;
int nc510_15=0;
int nc515=0;

int nc62=0;
int nc62_5=0;
int nc65_10=0;
int nc610_15=0;
int nc615=0;

int nc72=0;
int nc72_5=0;
int nc75_10=0;
int nc710_15=0;
int nc715=0;

int nc82=0;
int nc82_5=0;
int nc85_10=0;
int nc810_15=0;
int nc815=0;

int nc92=0;
int nc92_5=0;
int nc95_10=0;
int nc910_15=0;
int nc915=0;

int nc102=0;
int nc102_5=0;
int nc105_10=0;
int nc1010_15=0;
int nc1015=0;


int nLe22=0;
int nLe22_5=0;
int nLe25_10=0;
int nLe210_15=0;
int nLe215=0;

int nLe32=0;
int nLe32_5=0;
int nLe35_10=0;
int nLe310_15=0;
int nLe315=0;

int nLe42=0;
int nLe42_5=0;
int nLe45_10=0;
int nLe410_15=0;
int nLe415=0;

int nLe52=0;
int nLe52_5=0;
int nLe55_10=0;
int nLe510_15=0;
int nLe515=0;

int nLe62=0;
int nLe62_5=0;
int nLe65_10=0;
int nLe610_15=0;
int nLe615=0;

int nCh22=0;
int nCh22_5=0;
int nCh25_10=0;
int nCh210_15=0;
int nCh215=0;

int nCh32=0;
int nCh32_5=0;
int nCh35_10=0;
int nCh310_15=0;
int nCh315=0;

int nCh42=0;
int nCh42_5=0;
int nCh45_10=0;
int nCh410_15=0;
int nCh415=0;

int nCh52=0;
int nCh52_5=0;
int nCh55_10=0;
int nCh510_15=0;
int nCh515=0;

int nCh62=0;
int nCh62_5=0;
int nCh65_10=0;
int nCh610_15=0;
int nCh615=0;

int tr_sum=0;
int s3_sum=0;
int s8_sum=0;
int b4_sum=0;


int tr_new_sum=0;
int s3_new_sum=0;
int s8_new_sum=0;
int b4_new_sum=0;

int c5_sum=0;
int c6_sum=0;
int c7_sum=0;
int c8_sum=0;
int c9_sum=0;
int c10_sum=0;


int Le2_sum=0;
int Le3_sum=0;
int Le4_sum=0;
int Le5_sum=0;
int Le6_sum=0;
int Ch2_sum=0;
int Ch3_sum=0;
int Ch4_sum=0;
int Ch5_sum=0;
int Ch6_sum=0;


int div=div0[i];

vector<double>hx;
hx=Chebyshev_function();
hx.resize(hx.size());

vector<double>fx;
vector<double>Cotes(10,0.0);

for(int L=35;L>=0;L--)

{
fx.clear();
int m=L;
for(int i=L*(L+1)/2;i<m+L*(L+1)/2+1;i++) fx.push_back(hx[i]);
fx.resize(fx.size());

vector<double>gx;

for(int k=35;k>=0;k--)
{
gx.clear();
int n=k;
for(int i=k*(k+1)/2;i<n+k*(k+1)/2+1;i++) gx.push_back(hx[i]);
gx.resize(gx.size());



double ana=1.0;//anaは解析値を示す。
if( k==L) ana=PI/2.0;
if( k==0&&L==0) ana=PI;

// output
vector<double> tr_abs(div+1,0.0);// trapezoid 台形則
vector<double> s3_abs(div+1,0.0);// simpson　1/3則 
vector<double> s8_abs(div+1,0.0);// simpson　3/8則
vector<double> b4_abs(div+1,0.0);// Boole則  2/45


vector<double> tr_new_abs(div+1,0.0);// trapezoid 台形則
vector<double> s3_new_abs(div+1,0.0);// simpson　1/3則 
vector<double> s8_new_abs(div+1,0.0);// simpson　3/8則
vector<double> b4_new_abs(div+1,0.0);// Boole則  2/45
vector<double> c5_abs(div+1,0.0);
vector<double> c6_abs(div+1,0.0);
vector<double> c7_abs(div+1,0.0);
vector<double> c8_abs(div+1,0.0);
vector<double> c9_abs(div+1,0.0);
vector<double> c10_abs(div+1,0.0);


vector<double> Le2_abs(div+1,0.0);// Gauss-Legendre 2次 　
vector<double> Le3_abs(div+1,0.0);// Gauss-Legendre 3次
vector<double> Le4_abs(div+1,0.0);// Gauss-Legendre 4次
vector<double> Le5_abs(div+1,0.0);// Gauss-Legendre 5次
vector<double> Le6_abs(div+1,0.0);// Gauss-Legendre 6次

vector<double> Ch2_abs(div+1,0.0);// Chebyshev 2次 
vector<double> Ch3_abs(div+1,0.0);// Chebyshev 3次 
vector<double> Ch4_abs(div+1,0.0);// Chebyshev 4次 
vector<double> Ch5_abs(div+1,0.0);// Chebyshev 5次  
vector<double> Ch6_abs(div+1,0.0);// Chebyshev 6次 


double h=(x1-x0)/div;


double f_xn0=0.0;//分割始点
double f_xn2=0.0;//幅の1/4点
double f_xn3=0.0;//幅の1/3点
double f_xnm=0.0;//中間点
double f_xn6=0.0;//幅の2/3点
double f_xn7=0.0;//幅の3/4点
double f_xn1=0.0;//終点

double g_xn0=0.0;//分割始点
double g_xn2=0.0;//幅の1/4点
double g_xn3=0.0;//幅の1/3点
double g_xnm=0.0;//中間点
double g_xn6=0.0;//幅の2/3点
double g_xn7=0.0;//幅の3/4点
double g_xn1=0.0;//終点




double fg_xn0=0.0;
double fg_xnm=0.0;
double fg_xn1=0.0;

double tr_ort=0.0;// trapezoid 台形則
double s3_ort=0.0;// simpson　1/3則 
double s8_ort=0.0;// simpson　3/8則
double b4_ort=0.0;// Boole則 2/45

vector<double>sum_ini(10,0.0);

double Le2_ort=0.0;// Gauss-Legendre 2次 　
double Le3_ort=0.0;// Gauss-Legendre 3次
double Le4_ort=0.0;// Gauss-Legendre 4次
double Le5_ort=0.0;// Gauss-Legendre 5次
double Le6_ort=0.0;// Gauss-Legendre 6次

double Ch2_ort=0.0;// Chebyshev式 2次 
double Ch3_ort=0.0;// Chebyshev式 3次 
double Ch4_ort=0.0;// Chebyshev式 4次 
double Ch5_ort=0.0;// Chebyshev式 5次  
double Ch6_ort=0.0;// Chebyshev式 6次 



for(int j=0;j<div;j++)
{ 

Cotes=Newton_Cotes(div,j,m,n,x0,x1,fx,gx,sum_ini);
sum_ini=Cotes;


 //台形則、simpson則、Boole則　の積分
 vector<double>p_xn0(m+1,0.0);
 vector<double>p_xn2(m+1,0.0);
 vector<double>p_xn3(m+1,0.0);
 vector<double>p_xnm(m+1,0.0);
 vector<double>p_xn6(m+1,0.0);
 vector<double>p_xn7(m+1,0.0);
 vector<double>p_xn1(m+1,0.0);
 
 vector<double>q_xn0(n+1,0.0);
 vector<double>q_xn2(n+1,0.0);
 vector<double>q_xn3(n+1,0.0);
 vector<double>q_xnm(n+1,0.0);
 vector<double>q_xn6(n+1,0.0);
 vector<double>q_xn7(n+1,0.0);
 vector<double>q_xn1(n+1,0.0); 


  for(int i=0;i<m+1;i++)
 {
         p_xn0[i]=pow(cos(x0+j*h),i);
         p_xn2[i]=pow(cos(x0+j*h+h/4.0),i);
     p_xn3[i]=pow(cos(x0+j*h+h/3.0),i);
         p_xnm[i]=pow(cos(x0+j*h+h/2.0),i);
         p_xn6[i]=pow(cos(x0+j*h+2.0*h/3.0),i);
         p_xn7[i]=pow(cos(x0+j*h+3.0*h/4.0),i);
     p_xn1[i]=pow(cos(x0+j*h+h),i);
 }  
 f_xn0=inner_product(fx.begin(),fx.end(),p_xn0.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn2=inner_product(fx.begin(),fx.end(),p_xn2.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn3=inner_product(fx.begin(),fx.end(),p_xn3.begin(),0.0,plus<double>(),multiplies<double>());
 f_xnm=inner_product(fx.begin(),fx.end(),p_xnm.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn6=inner_product(fx.begin(),fx.end(),p_xn6.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn7=inner_product(fx.begin(),fx.end(),p_xn7.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn1=inner_product(fx.begin(),fx.end(),p_xn1.begin(),0.0,plus<double>(),multiplies<double>());


 for(int i=0;i<n+1;i++)
 {
         q_xn0[i]=pow(cos(x0+j*h),i);
         q_xn2[i]=pow(cos(x0+j*h+h/4.0),i);
     q_xn3[i]=pow(cos(x0+j*h+h/3.0),i);
         q_xnm[i]=pow(cos(x0+j*h+h/2.0),i);
         q_xn6[i]=pow(cos(x0+j*h+2.0*h/3.0),i);
         q_xn7[i]=pow(cos(x0+j*h+3.0*h/4.0),i);
     q_xn1[i]=pow(cos(x0+j*h+h),i);
 }  
 g_xn0=inner_product(gx.begin(),gx.end(),q_xn0.begin(),0.0,plus<double>(),multiplies<double>());
 g_xn2=inner_product(gx.begin(),gx.end(),q_xn2.begin(),0.0,plus<double>(),multiplies<double>());
 g_xn3=inner_product(gx.begin(),gx.end(),q_xn3.begin(),0.0,plus<double>(),multiplies<double>());
 g_xnm=inner_product(gx.begin(),gx.end(),q_xnm.begin(),0.0,plus<double>(),multiplies<double>());
 g_xn6=inner_product(gx.begin(),gx.end(),q_xn6.begin(),0.0,plus<double>(),multiplies<double>());
 g_xn7=inner_product(gx.begin(),gx.end(),q_xn7.begin(),0.0,plus<double>(),multiplies<double>());
 g_xn1=inner_product(gx.begin(),gx.end(),q_xn1.begin(),0.0,plus<double>(),multiplies<double>());

  
 fg_xn0=f_xn0*g_xn0;
 fg_xnm=f_xnm*g_xnm;
 fg_xn1=f_xn1*g_xn1;
 
 tr_ort=tr_ort+(fg_xn0+fg_xn1)*h/2.0;
 s3_ort=s3_ort+(fg_xn0+4.0*fg_xnm+fg_xn1)/3.0*h/2.0;  
 s8_ort=s8_ort+(fg_xn0+3.0*f_xn3*g_xn3+3.0*f_xn6*g_xn6+fg_xn1)*3.0/8.0*h/3.0;
 b4_ort=b4_ort+(7.0*fg_xn0+32.0*f_xn2*g_xn2+12.0*fg_xnm+32.0*f_xn7*g_xn7+7.0*fg_xn1)*2.0/45.0*h/4.0;



//Gauss-Legendre
//2分点
double xLe2_0=x0+j*h+h/2.0+h/2.0*x20;
double xLe2_1=x0+j*h+h/2.0+h/2.0*x21;

// 以下　次章に記載する　あるいは　後日に追加する　ので　削除


// 以上　次章に記載する　あるいは　後日に追加する　ので　削除 

double gCh6_0=0.0,gCh6_1=0.0,gCh6_2=0.0;
double gCh6_3=0.0,gCh6_4=0.0,gCh6_5=0.0;
for(int i=0;i<n+1;i++) 
 { 
  gCh6_0=gCh6_0+gx[i]*pow(cos(xCh6_0),i);
  gCh6_1=gCh6_1+gx[i]*pow(cos(xCh6_1),i);
  gCh6_2=gCh6_2+gx[i]*pow(cos(xCh6_2),i);
  gCh6_3=gCh6_3+gx[i]*pow(cos(xCh6_3),i);
  gCh6_4=gCh6_4+gx[i]*pow(cos(xCh6_4),i);
  gCh6_5=gCh6_5+gx[i]*pow(cos(xCh6_5),i);
 }

Ch6_ort=Ch6_ort+h/2.0*wCh6*(Ch6_0*gCh6_0+Ch6_1*gCh6_1+Ch6_2*gCh6_2+Ch6_3*gCh6_3+Ch6_4*gCh6_4+Ch6_5*gCh6_5);


}//div


if(k==L)
{
out002<<"p_"<<L<<"_"<<k<<","<<div<<","<<setprecision(20)
        <<tr_ort/ana<<","<<s3_ort/ana<<","<<s8_ort/ana<<","<<b4_ort/ana<<","<<" " <<","
        <<Cotes[0]/ana<<","<<Cotes[1]/ana<<","<<Cotes[2]/ana<<","<<Cotes[3]/ana<<","<<" "<<","
        <<Cotes[4]/ana<<","<<Cotes[5]/ana<<","<<Cotes[6]/ana<<","<<Cotes[7]/ana<<","
<<Cotes[8]/ana<<","<<Cotes[9]/ana<<","<<" " <<","
        <<Le2_ort/ana<<","<<Le3_ort/ana<<","<<Le4_ort/ana<<","<<Le5_ort/ana<<","<<Le6_ort/ana<<","<<" "<<","    
        <<Ch2_ort/ana<<","<<Ch3_ort/ana<<","<<Ch4_ort/ana<<","<<Ch5_ort/ana<<","<<Ch6_ort/ana<<","<<" "<<","
        <<ana<<endl;
}
else
{
out001<<"p_"<<L<<"_"<<k<<","<<div<<","<<setprecision(20)
        <<tr_ort/ana<<","<<s3_ort/ana<<","<<s8_ort/ana<<","<<b4_ort/ana<<","<<" "<<","
        <<Cotes[0]/ana<<","<<Cotes[1]/ana<<","<<Cotes[2]/ana<<","<<Cotes[3]/ana<<","<<" "<<","
        <<Cotes[4]/ana<<","<<Cotes[5]/ana<<","<<Cotes[6]/ana<<","<<Cotes[7]/ana<<","
<<Cotes[8]/ana<<","<<Cotes[9]/ana<<","<<" "<<","
        <<Le2_ort/ana<<","<<Le3_ort/ana<<","<<Le4_ort/ana<<","<<Le5_ort/ana<<","<<Le6_ort/ana<<","<<" "<<","
        <<Ch2_ort/ana<<","<<Ch3_ort/ana<<","<<Ch4_ort/ana<<","<<Ch5_ort/ana<<","<<Ch6_ort/ana<<","<<" "<<","
        <<ana<<endl;

if(abs(tr_ort)>=1.0e-2 ) ntr2=ntr2+1;
if(abs(tr_ort)<1.0e-2  && abs(tr_ort)>=1.0e-5) ntr2_5=ntr2_5+1;
if(abs(tr_ort)<1.0e-5 && abs(tr_ort)>=1.0e-10) ntr5_10=ntr5_10+1;
if(abs(tr_ort)<1.0e-10 && abs(tr_ort)>=1.0e-15)ntr10_15=ntr10_15+1;
if(abs(tr_ort)<1.0e-15) ntr15=ntr15+1;
tr_sum=ntr2+ntr2_5+ntr5_10+ntr10_15+ntr15;

if(abs(s3_ort)>=1.0e-2 ) ns32=ns32+1;
if(abs(s3_ort)<1.0e-2  && abs(s3_ort)>=1.0e-5) ns32_5=ns32_5+1;
if(abs(s3_ort)<1.0e-5 && abs(s3_ort)>=1.0e-10) ns35_10=ns35_10+1;
if(abs(s3_ort)<1.0e-10 && abs(s3_ort)>=1.0e-15) ns310_15=ns310_15+1;
if(abs(s3_ort)<1.0e-15) ns315=ns315+1;
s3_sum=ns32+ns32_5+ns35_10+ns310_15+ns315;

if(abs(s8_ort)>=1.0e-2 ) ns82=ns82+1;
if(abs(s8_ort)<1.0e-2  && abs(s8_ort)>=1.0e-5) ns82_5=ns82_5+1;
if(abs(s8_ort)<1.0e-5 && abs(s8_ort)>=1.0e-10) ns85_10=ns85_10+1;
if(abs(s8_ort)<1.0e-10 && abs(s8_ort)>=1.0e-15) ns810_15=ns810_15+1;
if(abs(s8_ort)<1.0e-15) ns815=ns815+1;
s8_sum=ns82+ns82_5+ns85_10+ns810_15+ns815;

if(abs(b4_ort)>=1.0e-2 ) nb42=nb42+1;
if(abs(b4_ort)<1.0e-2  && abs(b4_ort)>=1.0e-5) nb42_5=nb42_5+1;
if(abs(b4_ort)<1.0e-5 && abs(b4_ort)>=1.0e-10) nb45_10=nb45_10+1;
if(abs(b4_ort)<1.0e-10 && abs(b4_ort)>=1.0e-15) nb410_15=nb410_15+1;
if(abs(b4_ort)<1.0e-15) nb415=nb415+1;
b4_sum=nb42+nb42_5+nb45_10+nb410_15+nb415;


if(abs(Cotes[0])>=1.0e-2 ) ntr_new2=ntr_new2+1;
if(abs(Cotes[0])<1.0e-2  && abs(Cotes[0])>=1.0e-5) ntr_new2_5=ntr_new2_5+1;
if(abs(Cotes[0])<1.0e-5 && abs(Cotes[0])>=1.0e-10) ntr_new5_10=ntr_new5_10+1;
if(abs(Cotes[0])<1.0e-10 && abs(Cotes[0])>=1.0e-15)ntr_new10_15=ntr_new10_15+1;
if(abs(Cotes[0])<1.0e-15) ntr_new15=ntr_new15+1;
tr_new_sum=ntr_new2+ntr_new2_5+ntr_new5_10+ntr_new10_15+ntr_new15;

if(abs(Cotes[1])>=1.0e-2 ) ns3_new2=ns3_new2+1;
if(abs(Cotes[1])<1.0e-2  && abs(Cotes[1])>=1.0e-5) ns3_new2_5=ns3_new2_5+1;
if(abs(Cotes[1])<1.0e-5 && abs(Cotes[1])>=1.0e-10) ns3_new5_10=ns3_new5_10+1;
if(abs(Cotes[1])<1.0e-10 && abs(Cotes[1])>=1.0e-15) ns3_new10_15=ns3_new10_15+1;
if(abs(Cotes[1])<1.0e-15) ns3_new15=ns3_new15+1;
s3_new_sum=ns3_new2+ns3_new2_5+ns3_new5_10+ns3_new10_15+ns3_new15;

if(abs(Cotes[2])>=1.0e-2 ) ns8_new2=ns8_new2+1;
if(abs(Cotes[2])<1.0e-2  && abs(Cotes[2])>=1.0e-5) ns8_new2_5=ns8_new2_5+1;
if(abs(Cotes[2])<1.0e-5 && abs(Cotes[2])>=1.0e-10) ns8_new5_10=ns8_new5_10+1;
if(abs(Cotes[2])<1.0e-10 && abs(Cotes[2])>=1.0e-15) ns8_new10_15=ns8_new10_15+1;
if(abs(Cotes[2])<1.0e-15) ns8_new15=ns8_new15+1;
s8_new_sum=ns8_new2+ns8_new2_5+ns8_new5_10+ns8_new10_15+ns8_new15;

if(abs(Cotes[3])>=1.0e-2 ) nb4_new2=nb4_new2+1;
if(abs(Cotes[3])<1.0e-2  && abs(Cotes[3])>=1.0e-5) nb4_new2_5=nb4_new2_5+1;
if(abs(Cotes[3])<1.0e-5 && abs(Cotes[3])>=1.0e-10) nb4_new5_10=nb4_new5_10+1;
if(abs(Cotes[3])<1.0e-10 && abs(Cotes[3])>=1.0e-15) nb4_new10_15=nb4_new10_15+1;
if(abs(Cotes[3])<1.0e-15) nb4_new15=nb4_new15+1;
b4_new_sum=nb4_new2+nb4_new2_5+nb4_new5_10+nb4_new10_15+nb4_new15;


if(abs(Cotes[4])>=1.0e-2 ) nc52=nc52+1;
if(abs(Cotes[4])<1.0e-2  && abs(Cotes[4])>=1.0e-5) nc52_5=nc52_5+1;
if(abs(Cotes[4])<1.0e-5 && abs(Cotes[4])>=1.0e-10) nc55_10=nc55_10+1;
if(abs(Cotes[4])<1.0e-10 && abs(Cotes[4])>=1.0e-15) nc510_15=nc510_15+1;
if(abs(Cotes[4])<1.0e-15) nc515=nc515+1;
c5_sum=nc52+nc52_5+nc55_10+nc510_15+nc515;

if(abs(Cotes[5])>=1.0e-2 ) nc62=nc62+1;
if(abs(Cotes[5])<1.0e-2  && abs(Cotes[5])>=1.0e-5) nc62_5=nc62_5+1;
if(abs(Cotes[5])<1.0e-5 && abs(Cotes[5])>=1.0e-10) nc65_10=nc65_10+1;
if(abs(Cotes[5])<1.0e-10 && abs(Cotes[5])>=1.0e-15) nc610_15=nc610_15+1;
if(abs(Cotes[5])<1.0e-15) nc615=nc615+1;
c6_sum=nc62+nc62_5+nc65_10+nc610_15+nc615;

if(abs(Cotes[6])>=1.0e-2 ) nc72=nc72+1;
if(abs(Cotes[6])<1.0e-2  && abs(Cotes[6])>=1.0e-5) nc72_5=nc72_5+1;
if(abs(Cotes[6])<1.0e-5 && abs(Cotes[6])>=1.0e-10) nc75_10=nc75_10+1;
if(abs(Cotes[6])<1.0e-10 && abs(Cotes[6])>=1.0e-15) nc710_15=nc710_15+1;
if(abs(Cotes[6])<1.0e-15) nc715=nc715+1;
c7_sum=nc72+nc72_5+nc75_10+nc710_15+nc715;

if(abs(Cotes[7])>=1.0e-2 ) nc82=nc82+1;
if(abs(Cotes[7])<1.0e-2  && abs(Cotes[7])>=1.0e-5) nc82_5=nc82_5+1;
if(abs(Cotes[7])<1.0e-5 && abs(Cotes[7])>=1.0e-10) nc85_10=nc85_10+1;
if(abs(Cotes[7])<1.0e-10 && abs(Cotes[7])>=1.0e-15) nc810_15=nc810_15+1;
if(abs(Cotes[7])<1.0e-15) nc815=nc815+1;
c8_sum=nc82+nc82_5+nc85_10+nc810_15+nc815;

if(abs(Cotes[8])>=1.0e-2 ) nc92=nc92+1;
if(abs(Cotes[8])<1.0e-2  && abs(Cotes[8])>=1.0e-5) nc92_5=nc92_5+1;
if(abs(Cotes[8])<1.0e-5 && abs(Cotes[8])>=1.0e-10) nc95_10=nc95_10+1;
if(abs(Cotes[8])<1.0e-10 && abs(Cotes[8])>=1.0e-15) nc910_15=nc910_15+1;
if(abs(Cotes[8])<1.0e-15) nc915=nc915+1;
c9_sum=nc92+nc92_5+nc95_10+nc910_15+nc915;

if(abs(Cotes[9])>=1.0e-2 ) nc102=nc102+1;
if(abs(Cotes[9])<1.0e-2  && abs(Cotes[9])>=1.0e-5) nc102_5=nc102_5+1;
if(abs(Cotes[9])<1.0e-5 && abs(Cotes[9])>=1.0e-10) nc105_10=nc105_10+1;
if(abs(Cotes[9])<1.0e-10 && abs(Cotes[9])>=1.0e-15) nc1010_15=nc1010_15+1;
if(abs(Cotes[9])<1.0e-15) nc1015=nc1015+1;
c10_sum=nc102+nc102_5+nc105_10+nc1010_15+nc1015;


if(abs(Le2_ort)>=1.0e-2 ) nLe22=nLe22+1;
if(abs(Le2_ort)<1.0e-2  && abs(Le2_ort)>=1.0e-5) nLe22_5=nLe22_5+1;
if(abs(Le2_ort)<1.0e-5 && abs(Le2_ort)>=1.0e-10) nLe25_10=nLe25_10+1;
if(abs(Le2_ort)<1.0e-10 && abs(Le2_ort)>=1.0e-15) nLe210_15=nLe210_15+1;
if(abs(Le2_ort)<1.0e-15) nLe215=nLe215+1;
Le2_sum=nLe22+nLe22_5+nLe25_10+nLe210_15+nLe215;

if(abs(Le3_ort)>=1.0e-2 ) nLe32=nLe32+1;
if(abs(Le3_ort)<1.0e-2  && abs(Le3_ort)>=1.0e-5) nLe32_5=nLe32_5+1;
if(abs(Le3_ort)<1.0e-5 && abs(Le3_ort)>=1.0e-10) nLe35_10=nLe35_10+1;
if(abs(Le3_ort)<1.0e-10 && abs(Le3_ort)>=1.0e-15) nLe310_15=nLe310_15+1;
if(abs(Le3_ort)<1.0e-15) nLe315=nLe315+1;
Le3_sum=nLe32+nLe32_5+nLe35_10+nLe310_15+nLe315;

if(abs(Le4_ort)>=1.0e-2 ) nLe42=nLe42+1;
if(abs(Le4_ort)<1.0e-2  && abs(Le4_ort)>=1.0e-5) nLe42_5=nLe42_5+1;
if(abs(Le4_ort)<1.0e-5 && abs(Le4_ort)>=1.0e-10) nLe45_10=nLe45_10+1;
if(abs(Le4_ort)<1.0e-10 && abs(Le4_ort)>=1.0e-15) nLe410_15=nLe410_15+1;
if(abs(Le4_ort)<1.0e-15) nLe415=nLe415+1;
Le4_sum=nLe42+nLe42_5+nLe45_10+nLe410_15+nLe415;

if(abs(Le5_ort)>=1.0e-2 ) nLe52=nLe52+1;
if(abs(Le5_ort)<1.0e-2  && abs(Le5_ort)>=1.0e-5) nLe52_5=nLe52_5+1;
if(abs(Le5_ort)<1.0e-5 && abs(Le5_ort)>=1.0e-10) nLe55_10=nLe55_10+1;
if(abs(Le5_ort)<1.0e-10 && abs(Le5_ort)>=1.0e-15) nLe510_15=nLe510_15+1;
if(abs(Le5_ort)<1.0e-15) nLe515=nLe515+1;
Le5_sum=nLe52+nLe52_5+nLe55_10+nLe510_15+nLe515;

if(abs(Le6_ort)>=1.0e-2 ) nLe62=nLe62+1;
if(abs(Le6_ort)<1.0e-2  && abs(Le6_ort)>=1.0e-5) nLe62_5=nLe62_5+1;
if(abs(Le6_ort)<1.0e-5 && abs(Le6_ort)>=1.0e-10) nLe65_10=nLe65_10+1;
if(abs(Le6_ort)<1.0e-10 && abs(Le6_ort)>=1.0e-15) nLe610_15=nLe610_15+1;
if(abs(Le6_ort)<1.0e-15) nLe615=nLe615+1;
Le6_sum=nLe62+nLe62_5+nLe65_10+nLe610_15+nLe615;


if(abs(Ch2_ort)>=1.0e-2 ) nCh22=nCh22+1;
if(abs(Ch2_ort)<1.0e-2  && abs(Ch2_ort)>=1.0e-5) nCh22_5=nCh22_5+1;
if(abs(Ch2_ort)<1.0e-5 && abs(Ch2_ort)>=1.0e-10) nCh25_10=nCh25_10+1;
if(abs(Ch2_ort)<1.0e-10 && abs(Ch2_ort)>=1.0e-15) nCh210_15=nCh210_15+1;
if(abs(Ch2_ort)<1.0e-15) nCh215=nCh215+1;
Ch2_sum=nCh22+nCh22_5+nCh25_10+nCh210_15+nCh215;

if(abs(Ch3_ort)>=1.0e-2 ) nCh32=nCh32+1;
if(abs(Ch3_ort)<1.0e-2  && abs(Ch3_ort)>=1.0e-5) nCh32_5=nCh32_5+1;
if(abs(Ch3_ort)<1.0e-5 && abs(Ch3_ort)>=1.0e-10) nCh35_10=nCh35_10+1;
if(abs(Ch3_ort)<1.0e-10 && abs(Ch3_ort)>=1.0e-15) nCh310_15=nCh310_15+1;
if(abs(Ch3_ort)<1.0e-15) nCh315=nCh315+1;
Ch3_sum=nCh32+nCh32_5+nCh35_10+nCh310_15+nCh315;

if(abs(Ch4_ort)>=1.0e-2 ) nCh42=nCh42+1;
if(abs(Ch4_ort)<1.0e-2  && abs(Ch4_ort)>=1.0e-5)  nCh42_5=nCh42_5+1;
if(abs(Ch4_ort)<1.0e-5  && abs(Ch4_ort)>=1.0e-10) nCh45_10=nCh45_10+1;
if(abs(Ch4_ort)<1.0e-10 && abs(Ch4_ort)>=1.0e-15) nCh410_15=nCh410_15+1;
if(abs(Ch4_ort)<1.0e-15) nCh415=nCh415+1;
Ch4_sum=nCh42+nCh42_5+nCh45_10+nCh410_15+nCh415;

if(abs(Ch5_ort)>=1.0e-2 ) nCh52=nCh52+1;
if(abs(Ch5_ort)<1.0e-2  && abs(Ch5_ort)>=1.0e-5)  nCh52_5=nCh52_5+1;
if(abs(Ch5_ort)<1.0e-5  && abs(Ch5_ort)>=1.0e-10) nCh55_10=nCh55_10+1;
if(abs(Ch5_ort)<1.0e-10 && abs(Ch5_ort)>=1.0e-15) nCh510_15=nCh510_15+1;
if(abs(Ch5_ort)<1.0e-15) nCh515=nCh515+1;
Ch5_sum=nCh52+nCh52_5+nCh55_10+nCh510_15+nCh515;

if(abs(Ch6_ort)>=1.0e-2 ) nCh62=nCh62+1;
if(abs(Ch6_ort)<1.0e-2  && abs(Ch6_ort)>=1.0e-5)  nCh62_5=nCh62_5+1;
if(abs(Ch6_ort)<1.0e-5  && abs(Ch6_ort)>=1.0e-10) nCh65_10=nCh65_10+1;
if(abs(Ch6_ort)<1.0e-10 && abs(Ch6_ort)>=1.0e-15) nCh610_15=nCh610_15+1;
if(abs(Ch6_ort)<1.0e-15) nCh615=nCh615+1;
Ch6_sum=nCh62+nCh62_5+nCh65_10+nCh610_15+nCh615;
}

}//gx
out001<<"  "<<endl;
}//fx
out001.close();
out002<<"  "<<endl;
out002.close();

cout<<"div= "<<div<<endl;

out003<<"p_"<<"L"<<","<<div<<","
        <<tr_sum<<","<<ntr2<<","<<ntr2_5<<","<<ntr5_10<<","<<ntr10_15<<","<<ntr15<<","
        <<s3_sum<<","<<ns32<<","<<ns32_5<<","<<ns35_10<<","<<ns310_15<<","<<ns315<<","
        <<s8_sum<<","<<ns82<<","<<ns82_5<<","<<ns85_10<<","<<ns810_15<<","<<ns815<<","
        <<b4_sum<<","<<nb42<<","<<nb42_5<<","<<nb45_10<<","<<nb410_15<<","<<nb415<<","<<" "<<","

        <<tr_new_sum<<","<<ntr_new2<<","<<ntr_new2_5<<","<<ntr_new5_10<<","<<ntr_new10_15<<","<<ntr_new15<<","
        <<s3_new_sum<<","<<ns3_new2<<","<<ns3_new2_5<<","<<ns3_new5_10<<","<<ns3_new10_15<<","<<ns3_new15<<","
        <<s8_new_sum<<","<<ns8_new2<<","<<ns8_new2_5<<","<<ns8_new5_10<<","<<ns8_new10_15<<","<<ns8_new15<<","
        <<b4_new_sum<<","<<nb4_new2<<","<<nb4_new2_5<<","<<nb4_new5_10<<","<<nb4_new10_15<<","<<nb4_new15<<","<<" "<<","        

        <<c5_sum<<","<<nc52<<","<<nc52_5<<","<<nc55_10<<","<<nc510_15<<","<<nc515<<","
        <<c6_sum<<","<<nc62<<","<<nc62_5<<","<<nc65_10<<","<<nc610_15<<","<<nc615<<","
    <<c7_sum<<","<<nc72<<","<<nc72_5<<","<<nc75_10<<","<<nc710_15<<","<<nc715<<","
        <<c8_sum<<","<<nc82<<","<<nc82_5<<","<<nc85_10<<","<<nc810_15<<","<<nc815<<","
    <<c9_sum<<","<<nc92<<","<<nc92_5<<","<<nc95_10<<","<<nc910_15<<","<<nc915<<","
        <<c10_sum<<","<<nc102<<","<<nc102_5<<","<<nc105_10<<","<<nc1010_15<<","<<nc1015<<","<<" "<<","

        <<Le2_sum<<","<<nLe22<<","<<nLe22_5<<","<<nLe25_10<<","<<nLe210_15<<","<<nLe215<<","
        <<Le3_sum<<","<<nLe32<<","<<nLe32_5<<","<<nLe35_10<<","<<nLe310_15<<","<<nLe315<<","
        <<Le4_sum<<","<<nLe42<<","<<nLe42_5<<","<<nLe45_10<<","<<nLe410_15<<","<<nLe415<<","
        <<Le5_sum<<","<<nLe52<<","<<nLe52_5<<","<<nLe55_10<<","<<nLe510_15<<","<<nLe515<<","
        <<Le6_sum<<","<<nLe62<<","<<nLe62_5<<","<<nLe65_10<<","<<nLe610_15<<","<<nLe615<<","<<" "<<","
        
        <<Ch2_sum<<","<<nCh22<<","<<nCh22_5<<","<<nCh25_10<<","<<nCh210_15<<","<<nCh215<<","
        <<Ch3_sum<<","<<nCh32<<","<<nCh32_5<<","<<nCh35_10<<","<<nCh310_15<<","<<nCh315<<","
        <<Ch4_sum<<","<<nCh42<<","<<nCh42_5<<","<<nCh45_10<<","<<nCh410_15<<","<<nCh415<<","
        <<Ch5_sum<<","<<nCh52<<","<<nCh52_5<<","<<nCh55_10<<","<<nCh510_15<<","<<nCh515<<","
        <<Ch6_sum<<","<<nCh62<<","<<nCh62_5<<","<<nCh65_10<<","<<nCh610_15<<","<<nCh615<<","
        <<endl;

}// div0[i]
out003.close();



return 0;
}

vector<double> Chebyshev_function()
{
//Chebyshev関数
vector<long double >t0(0+1,0.0);
t0[0]=1.0;

// 以下　コード　C-1 に同じ



// 以上　C-1 に同じ

t35[34]=0.0;
t35[35]=17179869184.0;


int k;
vector<double>hx;
k=0;for(int i=0;i<k+1;i++)      hx.push_back(t0[i]);
k=1;for(int i=0;i<k+1;i++)      hx.push_back(t1[i]);
// 以下　繰り返し　で削除 


// 以上　繰り返し　で　削除

k=35;for(int i=0;i<k+1;i++)     hx.push_back(t35[i]);
hx.resize(hx.size());

return hx;

}



vector<double>Newton_Cotes(int div,int j,int m,int n,double x_start, double x_end,
vector<double>fx,vector<double>gx,vector<double>sum_ini)
{

double f_xn00=0.0;//分割始点
double f_xn10=0.0;//幅の1/10点

//以下 次章に記載する　あるいは　後日に追加する　ので削除


// 以上　次章に記載する　あるいは　後日に追加する　ので、削除

vector<double>Cotes_function(10,0.0);

Cotes_function[0]=tr_new;
Cotes_function[1]=s3_new;
Cotes_function[2]=s8_new;
Cotes_function[3]=b4_new;
Cotes_function[4]=c5_new;
Cotes_function[5]=c6_new;
Cotes_function[6]=c7_new;
Cotes_function[7]=c8_new;
Cotes_function[8]=c9_new;
Cotes_function[9]=c10_new;

return Cotes_function;

}


本章 7章の説明へ



5、Legendre 多項式による級数展開・11 次 Chebyshev 多項式への適用 (コード D-1)

#include <cmath>
#include <fstream>
#include <vector>
#include <iomanip>
#include <numeric>
#include <iostream>
using namespace std;

const long double PI=3.14159265358979323846264338327950288;

vector<double> Legendre_function();

//Legendre多項式による多項式展開
int main()
{

vector<double>hx;
hx=Legendre_function();
hx.resize(hx.size());

//Legendre多項式展開を行う被対象の11次Chebyshev関数 
vector<long double>t11(11+1,0.0);
t11[0]=0.0;
t11[1]=-11.0;
t11[2]=0.0;
t11[3]=220.0;
t11[4]=0.0;
t11[5]=-1232;
t11[6]=0.0;
t11[7]=2816.0; 
t11[8]=0.0;
t11[9]=-2816.0;
t11[10]=0.0;
t11[11]=1024.0;


vector<long double>gx;
gx=t11;
gx.resize(gx.size());
int n=(int)gx.size();//被対象関数の次数

//Gauss-Legendre
//2分点
double x20=-1.0/sqrt(3.0);
double x21=1.0/sqrt(3.0);
//重み係数
double wLe2_0=1.0;
double wLe2_1=1.0;

//　以下　次章に記載する　あるいは後日に記載する　ので　削除


// 以上　次章に記載する　あるいは　後日に記載する　ので　削除

// 6 分点　重み 1/3    

double xCh65=0.86624681810782;
double wCh6=1.0/3.0;


//区間分割数
vector<int>div0(24,0);
div0[0]=1;
div0[1]=2;
div0[2]=3;
div0[3]=4;
div0[4]=6;

div0[5]=10;
div0[6]=16;
div0[7]=25;
div0[8]=32;
div0[9]=40;

div0[10]=63;
div0[11]=100;
div0[12]=160;
div0[13]=250;
div0[14]=320;

div0[15]=400;
div0[16]=630;
div0[17]=1000;
div0[18]=1600;
div0[19]=2500;
div0[20]=3200;
div0[21]=4000;
div0[22]=6300;
div0[23]=10000;


//a0,a1,..,anの係数用積分区間
double x0=-1.0;
double x1=1.0; 

for(int i=0;i<(int)div0.size();i++)
{
int div=div0[i];
vector<long double>fx;

int ak=12;//展開するLegendre関数の次数

//an値の格納部分
vector<long double>tr_an(ak+1,0.0),s3_an(ak+1,0.0);
vector<long double>s8_an(ak+1,0.0),b2_an(ak+1,0.0);
vector<long double>Le2_an(ak+1,0.0),Le3_an(ak+1,0.0);
vector<long double>Le4_an(ak+1,0.0),Le5_an(ak+1,0.0);
vector<long double>Le6_an(ak+1,0.0),Ch2_an(ak+1,0.0);
vector<long double>Ch3_an(ak+1,0.0),Ch4_an(ak+1,0.0);
vector<long double>Ch5_an(ak+1,0.0),Ch6_an(ak+1,0.0);

for(int L=ak;L>=0;L--)
{
fx.clear();
int m=L;
for(int i=L*(L+1)/2;i<m+L*(L+1)/2+1;i++) fx.push_back(hx[i]);
fx.resize(fx.size());

double factor=(2.0*L+1)/2.0;//Legendreの直交係数の逆数

double h=(x1-x0)/div;
double f_xn0=0.0;//分割始点
double f_xn2=0.0;//幅の1/4点
double f_xn3=0.0;//幅の1/3点
double f_xnm=0.0;//中間点
double f_xn6=0.0;//幅の2/3点
double f_xn7=0.0;//幅の3/4点
double f_xn1=0.0;//終点

double g_xn0=0.0;//分割始点
double g_xn2=0.0;//幅の1/4点
double g_xn3=0.0;//幅の1/3点
double g_xnm=0.0;//中間点
double g_xn6=0.0;//幅の2/3点
double g_xn7=0.0;//幅の3/4点
double g_xn1=0.0;//終点

double fg_xn0=0.0;
double fg_xnm=0.0;
double fg_xn1=0.0;

double tr_ort=0.0;// trapezoid 台形則
double s3_ort=0.0;// simpson　1/3則 
double s8_ort=0.0;// simpson　3/8則
double b2_ort=0.0;// Boole則 2/45

double Le2_ort=0.0;// Gauss-Legendre 2次 　
double Le3_ort=0.0;// Gauss-Legendre 3次
double Le4_ort=0.0;// Gauss-Legendre 4次
double Le5_ort=0.0;// Gauss-Legendre 5次
double Le6_ort=0.0;// Gauss-Legendre 6次

double Ch2_ort=0.0;// Chebyshev式 2次 
double Ch3_ort=0.0;// Chebyshev式 3次 
double Ch4_ort=0.0;// Chebyshev式 4次 
double Ch5_ort=0.0;// Chebyshev式 5次  
double Ch6_ort=0.0;// Chebyshev式 6次 


for(int j=0;j<div;j++)
{ 

 //台形則、simpson則、Boole則
 vector<double>p_xn0(m+1,0.0);
 vector<double>p_xn2(m+1,0.0);
 vector<double>p_xn3(m+1,0.0);
 vector<double>p_xnm(m+1,0.0);
 vector<double>p_xn6(m+1,0.0);
 vector<double>p_xn7(m+1,0.0);
 vector<double>p_xn1(m+1,0.0);
 
 vector<double>q_xn0(n+1,0.0);
 vector<double>q_xn2(n+1,0.0);
 vector<double>q_xn3(n+1,0.0);
 vector<double>q_xnm(n+1,0.0);
 vector<double>q_xn6(n+1,0.0);
 vector<double>q_xn7(n+1,0.0);
 vector<double>q_xn1(n+1,0.0);

  for(int i=0;i<m+1;i++)
 {
         p_xn0[i]=pow(x0+j*h,i);
         p_xn2[i]=pow(x0+j*h+h/4.0,i);
     p_xn3[i]=pow(x0+j*h+h/3.0,i);
         p_xnm[i]=pow(x0+j*h+h/2.0,i);
         p_xn6[i]=pow(x0+j*h+2.0*h/3.0,i);
         p_xn7[i]=pow(x0+j*h+3.0*h/4.0,i);
     p_xn1[i]=pow(x0+j*h+h,i);
 }  
 f_xn0=inner_product(fx.begin(),fx.end(),p_xn0.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn2=inner_product(fx.begin(),fx.end(),p_xn2.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn3=inner_product(fx.begin(),fx.end(),p_xn3.begin(),0.0,plus<double>(),multiplies<double>());
 f_xnm=inner_product(fx.begin(),fx.end(),p_xnm.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn6=inner_product(fx.begin(),fx.end(),p_xn6.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn7=inner_product(fx.begin(),fx.end(),p_xn7.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn1=inner_product(fx.begin(),fx.end(),p_xn1.begin(),0.0,plus<double>(),multiplies<double>());
 
 for(int i=0;i<n;i++)
 {
         q_xn0[i]=pow(x0+j*h,i);
         q_xn2[i]=pow(x0+j*h+h/4.0,i);
     q_xn3[i]=pow(x0+j*h+h/3.0,i);
         q_xnm[i]=pow(x0+j*h+h/2.0,i);
         q_xn6[i]=pow(x0+j*h+2.0*h/3.0,i);
         q_xn7[i]=pow(x0+j*h+3.0*h/4.0,i);
     q_xn1[i]=pow(x0+j*h+h,i);
 }  
 g_xn0=inner_product(gx.begin(),gx.end(),q_xn0.begin(),0.0,plus<double>(),multiplies<double>());
 g_xn2=inner_product(gx.begin(),gx.end(),q_xn2.begin(),0.0,plus<double>(),multiplies<double>());
 g_xn3=inner_product(gx.begin(),gx.end(),q_xn3.begin(),0.0,plus<double>(),multiplies<double>());
 g_xnm=inner_product(gx.begin(),gx.end(),q_xnm.begin(),0.0,plus<double>(),multiplies<double>());
 g_xn6=inner_product(gx.begin(),gx.end(),q_xn6.begin(),0.0,plus<double>(),multiplies<double>());
 g_xn7=inner_product(gx.begin(),gx.end(),q_xn7.begin(),0.0,plus<double>(),multiplies<double>());
 g_xn1=inner_product(gx.begin(),gx.end(),q_xn1.begin(),0.0,plus<double>(),multiplies<double>());
  
 fg_xn0=f_xn0*g_xn0;
 fg_xnm=f_xnm*g_xnm;
 fg_xn1=f_xn1*g_xn1;
 
 tr_ort=tr_ort+(fg_xn0+fg_xn1)*h/2.0;
 s3_ort=s3_ort+(fg_xn0+4.0*fg_xnm+fg_xn1)/3.0*h/2.0;  
 s8_ort=s8_ort+(fg_xn0+3.0*f_xn3*g_xn3+3.0*f_xn6*g_xn6+fg_xn1)*3.0/8.0*h/3.0;
 b2_ort=b2_ort+(7.0*fg_xn0+32.0*f_xn2*g_xn2+12.0*fg_xnm+32.0*f_xn7*g_xn7+7.0*fg_xn1)*2.0/45.0*h/4.0;  

//Gauss-Legendre
//2分点
double xLe2_0=x0+j*h+h/2.0+h/2.0*x20;
double xLe2_1=x0+j*h+h/2.0+h/2.0*x21;
double Le2_0=0.0,Le2_1=0.0;

for(int i=0;i<m+1;i++) 
 { 
  Le2_0=Le2_0+fx[i]*pow(xLe2_0,i);
  Le2_1=Le2_1+fx[i]*pow(xLe2_1,i); 
 }

double gLe2_0=0.0,gLe2_1=0.0;
for(int i=0;i<n;i++) 
 { 
  gLe2_0=gLe2_0+gx[i]*pow(xLe2_0,i);
  gLe2_1=gLe2_1+gx[i]*pow(xLe2_1,i); 
 }

Le2_ort=Le2_ort+h/2.0*(wLe2_0*Le2_0*gLe2_0+wLe2_1*Le2_1*gLe2_1);

// 以下　次章に記載する　あるいは　後日に追加する　ので　削除


// 以上 次章に記載する　あるいは　後日に追加する　ので　削除

double gCh6_0=0.0,gCh6_1=0.0,gCh6_2=0.0,gCh6_3=0.0,gCh6_4=0.0,gCh6_5=0.0;

for(int i=0;i<n;i++) 
 { 
  gCh6_0=gCh6_0+gx[i]*pow(xCh6_0,i);
  gCh6_1=gCh6_1+gx[i]*pow(xCh6_1,i);
  gCh6_2=gCh6_2+gx[i]*pow(xCh6_2,i);
  gCh6_3=gCh6_3+gx[i]*pow(xCh6_3,i);
  gCh6_4=gCh6_4+gx[i]*pow(xCh6_4,i);
  gCh6_5=gCh6_5+gx[i]*pow(xCh6_5,i);
 }

Ch6_ort=Ch6_ort+h/2.0*wCh6*(Ch6_0*gCh6_0+Ch6_1*gCh6_1+Ch6_2*gCh6_2+Ch6_3*gCh6_3+Ch6_4*gCh6_4+Ch6_5*gCh6_5);

}//div

cout<<"p_"<<L<<","<<div<<endl;

tr_an[L]=tr_ort*factor;
s3_an[L]=s3_ort*factor;  
s8_an[L]=s8_ort*factor;
b2_an[L]=b2_ort*factor;
Le2_an[L]=Le2_ort*factor;
Le3_an[L]=Le3_ort*factor;
Le4_an[L]=Le4_ort*factor;
Le5_an[L]=Le5_ort*factor;
Le6_an[L]=Le6_ort*factor;
Ch2_an[L]=Ch2_ort*factor;
Ch3_an[L]=Ch3_ort*factor;
Ch4_an[L]=Ch4_ort*factor;
Ch5_an[L]=Ch5_ort*factor;
Ch6_an[L]=Ch6_ort*factor;

}//fxの繰り返しに対応

fstream out00an("an_Legngrepoly.csv",ios::out 
        |ios::binary |ios::app);
out00an<<"p_"<<"L"<<","<<"div"<<","<<"tr_an"<<","<<"s3_an"<<","<<"s8_an"<<","<<"b2_an"<<","
        <<"Le2_an"<<","<<"Le3_an"<<","<<"Le4_an"<<","<<"Le5_an"<<","<<"Le6_an"<<","<<"Ch2_an"<<","
        <<"Ch3_an"<<","<<"Ch4_an"<<","<<"Ch5_an"<<","
        <<"Ch6_an"<<endl;

for(int L=ak;L>=0;L--) out00an<<"p_"<<L<<","<<div<<","<<setprecision(20)<<tr_an[L]<<","<<s3_an[L]<<","
        <<s8_an[L]<<","<<b2_an[L]<<","<<Le2_an[L]<<","<<Le3_an[L]<<","<<Le4_an[L]<<","<<Le5_an[L]<<","
        <<Le6_an[L]<<","<<Ch2_an[L]<<","<<Ch3_an[L]<<","<<Ch4_an[L]<<","<<Ch5_an[L]<<","<<Ch6_an[L]<<endl;

out00an<<" "<<endl;
out00an.close();

vector<long double>xn(gx.size(),0.0);
long double x=0.0;
int kk=200+1;
vector<long double>gx_value(kk,0.0);
for(int j=0;j<kk;j++)
{
 x=0.03*j-3.0;
 for(int jj=0;jj<(int)gx.size();jj++)xn[jj]=pow(x,(long double)jj);
 gx_value[j]=inner_product(gx.begin(),gx.end(),xn.begin(),0.0,plus<long double>(),multiplies<long double>());
}

vector<long double>re_Le6(kk,0.0);
vector<long double>re_Le5(kk,0.0);
vector<long double>re_Le4(kk,0.0);
vector<long double>re_Le3(kk,0.0);
vector<long double>re_Le2(kk,0.0);

vector<long double>re_Ch6(kk,0.0);
vector<long double>re_Ch5(kk,0.0);
vector<long double>re_Ch4(kk,0.0);
vector<long double>re_Ch3(kk,0.0);
vector<long double>re_Ch2(kk,0.0);

vector<long double>re_b2(kk,0.0);
vector<long double>re_s8(kk,0.0);
vector<long double>re_s3(kk,0.0);
vector<long double>re_tr(kk,0.0);


for(int j=0;j<kk;j++)
{
        x=0.03*j-3.0;
        long double Le6_sum=0.0,Le5_sum=0.0,Le4_sum=0.0,Le3_sum=0.0,Le2_sum=0.0;
        long double Ch6_sum=0.0,Ch5_sum=0.0,Ch4_sum=0.0,Ch3_sum=0.0,Ch2_sum=0.0;
        long double b2_sum=0.0,s8_sum=0.0,s3_sum=0.0,tr_sum=0.0;

        for(int L=ak;L>=0;L--)
    {
    fx.clear();
    int m=L;
    for(int i=L*(L+1)/2;i<m+L*(L+1)/2+1;i++) fx.push_back(hx[i]);
    fx.resize(fx.size());       
        for(int i=0;i<m+1;i++)
        {
         Le6_sum=Le6_sum+Le6_an[L]*fx[i]*pow(x,i);
         Le5_sum=Le5_sum+Le5_an[L]*fx[i]*pow(x,i);
         Le4_sum=Le4_sum+Le4_an[L]*fx[i]*pow(x,i);
         Le3_sum=Le3_sum+Le3_an[L]*fx[i]*pow(x,i);
         Le2_sum=Le2_sum+Le2_an[L]*fx[i]*pow(x,i);

         Ch6_sum=Ch6_sum+Ch6_an[L]*fx[i]*pow(x,i);
         Ch5_sum=Ch5_sum+Ch5_an[L]*fx[i]*pow(x,i);
         Ch4_sum=Ch4_sum+Ch4_an[L]*fx[i]*pow(x,i);
         Ch3_sum=Ch3_sum+Ch3_an[L]*fx[i]*pow(x,i);
         Ch2_sum=Ch2_sum+Ch2_an[L]*fx[i]*pow(x,i);

         b2_sum=b2_sum+b2_an[L]*fx[i]*pow(x,i);
         s8_sum=s8_sum+s8_an[L]*fx[i]*pow(x,i);
         s3_sum=s3_sum+s3_an[L]*fx[i]*pow(x,i);
         tr_sum=tr_sum+tr_an[L]*fx[i]*pow(x,i);

        }               
        }
        re_Le6[j]=Le6_sum;
        re_Le5[j]=Le5_sum;
        re_Le4[j]=Le4_sum;
        re_Le3[j]=Le3_sum;
        re_Le2[j]=Le2_sum;

        re_Ch6[j]=Ch6_sum;
        re_Ch5[j]=Ch5_sum;
        re_Ch4[j]=Ch4_sum;
        re_Ch3[j]=Ch3_sum;
        re_Ch2[j]=Ch2_sum;

        re_b2[j]=b2_sum;
        re_s8[j]=s8_sum;
        re_s3[j]=s3_sum;
        re_tr[j]=tr_sum;

}

fstream outrecalc("Re-calculation_result.csv"
        ,ios::out |ios::binary  |ios::app);

outrecalc<<"div"<<","<<"j"<<","<<"0.03*j-3.0"<<","<<"re_Le6"<<","<<"re_Le5"<<","<<"re_Le4"<<","
        <<"re_Le3"<<","<<"re_Le2"<<","<<"re_Ch6"<<","<<"re_Ch5"<<","<<"re_Ch4"<<","<<"re_Ch3"<<","
        <<"re_Ch2"<<","<<"re_b2"<<","<<"re_s8"<<","<<"re_s3"<<","<<"re_tr"<<","<<"gx_value"<<","
        <<"gx_value-re_Le6"<<endl;

for(int j=0;j<(int)re_Le6.size();j++) 
        outrecalc<<div<<","<<setw(3)<<j<<","<<0.03*j-3.0<<","<<setprecision(20)<<re_Le6[j]<<","<<re_Le5[j]
<<","<<re_Le4[j]<<","<<re_Le3[j]<<","<<re_Le2[j]<<","<<re_Ch6[j]<<","<<re_Ch5[j]<<","<<re_Ch4[j]<<","
        <<re_Ch3[j]<<","<<re_Ch2[j]<<","<<re_b2[j]<<","<<re_s8[j]<<","<<re_s3[j]<<","<<re_tr[j]<<","
        <<gx_value[j]<<","<<gx_value[j]-re_Le6[j]<<endl;

outrecalc<<" "<<endl;
outrecalc.close();

re_Le6.clear();
re_Le5.clear();
re_Le4.clear();
re_Le3.clear();
re_Le2.clear();

re_Ch6.clear();
re_Ch5.clear();
re_Ch4.clear();
re_Ch3.clear();
re_Ch2.clear();

re_b2.clear();
re_s8.clear();
re_s3.clear();
re_tr.clear();

}// div0[i]に対応

return 0;
}

vector<double> Legendre_function()
{
//Legendre関数p　
vector<double >p0(0+1,0.0);
p0[0]=1.0;

// 以下、コード　L-1 と同じ故に削除


// 以上　コード　L-1 と同じ故に、削除 

p34[33]=0.0;
p34[34]=7113260368810144185/4294967296.0;


int k;
vector<double>hx;
k=0;for(int i=0;i<k+1;i++)      hx.push_back(p0[i]);
k=1;for(int i=0;i<k+1;i++)      hx.push_back(p1[i]);

// 以下　繰り返し故に　削除



// 以上　繰り返し故に削除

k=34;for(int i=0;i<k+1;i++)     hx.push_back(p34[i]);
hx.resize(hx.size());

return hx;

}


本章 7章の説明へ



6、Legendre 多項式による級数展開　sin( πx ) での適用(コード D-2)　

#include <cmath>
#include <fstream>
#include <vector>
#include <iomanip>
#include <numeric>
#include <iostream>
using namespace std;

const long double PI=3.14159265358979323846264338327950288;

vector<double> Legendre_function();

double g_function(double x,double a, double b) 
{
         return sin(PI*x);
}

//Legendre多項式による多項式展開
int main()
{

vector<double>hx;
hx=Legendre_function();
hx.resize(hx.size());

double a=0.0;
double b=0.0;

//Gauss-Legendre
//2分点
double x20=-1.0/sqrt(3.0);
double x21=1.0/sqrt(3.0);
//重み係数
double wLe2_0=1.0;
double wLe2_1=1.0;

//　以下　次章に記載する　あるいは後日に記載する　ので　削除


// 以上　次章に記載する　あるいは　後日に記載する　ので　削除

// 6 分点　重み 1/3    
double xCh60=-0.86624681810782;
double xCh61=-0.422518653761111;
double xCh62=-0.266635401516705;
double xCh63=0.266635401516705;
double xCh64=0.422518653761111;
double xCh65=0.86624681810782;
double wCh6=1.0/3.0;


//区間分割数
vector<int>div0(24,0);
div0[0]=1;
div0[1]=2;
div0[2]=3;
div0[3]=4;
div0[4]=6;

div0[5]=10;
div0[6]=16;
div0[7]=25;
div0[8]=32;
div0[9]=40;

div0[10]=63;
div0[11]=100;
div0[12]=160;
div0[13]=250;
div0[14]=320;

div0[15]=400;
div0[16]=630;
div0[17]=1000;
div0[18]=1600;
div0[19]=2500;
div0[20]=3200;
div0[21]=4000;
div0[22]=6300;
div0[23]=10000;


//a0,a1,..,anの係数用積分区間
double x0=-1.0;
double x1=1.0; 

for(int i=0;i<(int)div0.size();i++)
{
int div=div0[i];
vector<long double>fx;

int ak=23;//展開するLegendre関数の次数

//an値の格納部分
vector<long double>tr_an(ak+1,0.0),s3_an(ak+1,0.0);
vector<long double>s8_an(ak+1,0.0),b2_an(ak+1,0.0);
vector<long double>Le2_an(ak+1,0.0),Le3_an(ak+1,0.0);
vector<long double>Le4_an(ak+1,0.0),Le5_an(ak+1,0.0);
vector<long double>Le6_an(ak+1,0.0),Ch2_an(ak+1,0.0);
vector<long double>Ch3_an(ak+1,0.0),Ch4_an(ak+1,0.0);
vector<long double>Ch5_an(ak+1,0.0),Ch6_an(ak+1,0.0);

for(int L=ak;L>=0;L--)
{
fx.clear();
int m=L;
for(int i=L*(L+1)/2;i<m+L*(L+1)/2+1;i++) fx.push_back(hx[i]);
fx.resize(fx.size());

double factor=(2.0*L+1)/2.0;//Legendreの直交係数の逆数

double h=(x1-x0)/div;
double f_xn0=0.0;//分割始点
double f_xn2=0.0;//幅の1/4点
double f_xn3=0.0;//幅の1/3点
double f_xnm=0.0;//中間点
double f_xn6=0.0;//幅の2/3点
double f_xn7=0.0;//幅の3/4点
double f_xn1=0.0;//終点

double g_xn0=0.0;//分割始点
double g_xn2=0.0;//幅の1/4点
double g_xn3=0.0;//幅の1/3点
double g_xnm=0.0;//中間点
double g_xn6=0.0;//幅の2/3点
double g_xn7=0.0;//幅の3/4点
double g_xn1=0.0;//終点

double fg_xn0=0.0;
double fg_xnm=0.0;
double fg_xn1=0.0;

double tr_ort=0.0;// trapezoid 台形則
double s3_ort=0.0;// simpson　1/3則 
double s8_ort=0.0;// simpson　3/8則
double b2_ort=0.0;// Boole則 2/45

double Le2_ort=0.0;// Gauss-Legendre 2次 　
double Le3_ort=0.0;// Gauss-Legendre 3次
double Le4_ort=0.0;// Gauss-Legendre 4次
double Le5_ort=0.0;// Gauss-Legendre 5次
double Le6_ort=0.0;// Gauss-Legendre 6次

double Ch2_ort=0.0;// Chebyshev式 2次 
double Ch3_ort=0.0;// Chebyshev式 3次 
double Ch4_ort=0.0;// Chebyshev式 4次 
double Ch5_ort=0.0;// Chebyshev式 5次  
double Ch6_ort=0.0;// Chebyshev式 6次 


for(int j=0;j<div;j++)
{ 

 //台形則、simpson則、Boole則
 vector<double>p_xn0(m+1,0.0);
 vector<double>p_xn2(m+1,0.0);
 vector<double>p_xn3(m+1,0.0);
 vector<double>p_xnm(m+1,0.0);
 vector<double>p_xn6(m+1,0.0);
 vector<double>p_xn7(m+1,0.0);
 vector<double>p_xn1(m+1,0.0);
 
 

  for(int i=0;i<m+1;i++)
 {
         p_xn0[i]=pow(x0+j*h,i);
         p_xn2[i]=pow(x0+j*h+h/4.0,i);
     p_xn3[i]=pow(x0+j*h+h/3.0,i);
         p_xnm[i]=pow(x0+j*h+h/2.0,i);
         p_xn6[i]=pow(x0+j*h+2.0*h/3.0,i);
         p_xn7[i]=pow(x0+j*h+3.0*h/4.0,i);
     p_xn1[i]=pow(x0+j*h+h,i);
 }  
 f_xn0=inner_product(fx.begin(),fx.end(),p_xn0.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn2=inner_product(fx.begin(),fx.end(),p_xn2.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn3=inner_product(fx.begin(),fx.end(),p_xn3.begin(),0.0,plus<double>(),multiplies<double>());
 f_xnm=inner_product(fx.begin(),fx.end(),p_xnm.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn6=inner_product(fx.begin(),fx.end(),p_xn6.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn7=inner_product(fx.begin(),fx.end(),p_xn7.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn1=inner_product(fx.begin(),fx.end(),p_xn1.begin(),0.0,plus<double>(),multiplies<double>());
 
 g_xn0=g_function(x0+j*h,a,b);
 g_xn2=g_function(x0+j*h+h/4.0,a,b);
 g_xn3=g_function(x0+j*h+h/3.0,a,b);
 g_xnm=g_function(x0+j*h+h/2.0,a,b);
 g_xn6=g_function(x0+j*h+2.0*h/3.0,a,b);
 g_xn7=g_function(x0+j*h+3.0*h/4.0,a,b);
 g_xn1=g_function(x0+j*h+h,a,b);

 fg_xn0=f_xn0*g_xn0;
 fg_xnm=f_xnm*g_xnm;
 fg_xn1=f_xn1*g_xn1;
 
 tr_ort=tr_ort+(fg_xn0+fg_xn1)*h/2.0;
 s3_ort=s3_ort+(fg_xn0+4.0*fg_xnm+fg_xn1)/3.0*h/2.0;  
 s8_ort=s8_ort+(fg_xn0+3.0*f_xn3*g_xn3+3.0*f_xn6*g_xn6+fg_xn1)*3.0/8.0*h/3.0;
 b2_ort=b2_ort+(7.0*fg_xn0+32.0*f_xn2*g_xn2+12.0*fg_xnm+32.0*f_xn7*g_xn7+7.0*fg_xn1)*2.0/45.0*h/4.0;  

//Gauss-Legendre
//2分点
double xLe2_0=x0+j*h+h/2.0+h/2.0*x20;
double xLe2_1=x0+j*h+h/2.0+h/2.0*x21;

double Le2_0=0.0,Le2_1=0.0;
for(int i=0;i<m+1;i++) 
 { 
  Le2_0=Le2_0+fx[i]*pow(xLe2_0,i);
  Le2_1=Le2_1+fx[i]*pow(xLe2_1,i); 
 }

double gLe2_0=0.0,gLe2_1=0.0;
gLe2_0=g_function(xLe2_0,a,b);
gLe2_1=g_function(xLe2_1,a,b); 

Le2_ort=Le2_ort+h/2.0*(wLe2_0*Le2_0*gLe2_0+wLe2_1*Le2_1*gLe2_1);

// 以下　次章に記載する　あるいは　後日に追加する　ので　削除


// 以上 次章に記載する　あるいは　後日に追加する　ので　削除

gCh6_1=g_function(xCh6_1,a,b);
gCh6_2=g_function(xCh6_2,a,b);
gCh6_3=g_function(xCh6_3,a,b);
gCh6_4=g_function(xCh6_4,a,b);
gCh6_5=g_function(xCh6_5,a,b);

Ch6_ort=Ch6_ort+h/2.0*wCh6*(Ch6_0*gCh6_0+Ch6_1*gCh6_1+Ch6_2*gCh6_2+Ch6_3*gCh6_3+Ch6_4*gCh6_4+Ch6_5*gCh6_5);

}//div



cout<<"p_"<<L<<","<<div<<endl;

tr_an[L]=tr_ort*factor;
s3_an[L]=s3_ort*factor;  
s8_an[L]=s8_ort*factor;
b2_an[L]=b2_ort*factor;
Le2_an[L]=Le2_ort*factor;
Le3_an[L]=Le3_ort*factor;
Le4_an[L]=Le4_ort*factor;
Le5_an[L]=Le5_ort*factor;
Le6_an[L]=Le6_ort*factor;
Ch2_an[L]=Ch2_ort*factor;
Ch3_an[L]=Ch3_ort*factor;
Ch4_an[L]=Ch4_ort*factor;
Ch5_an[L]=Ch5_ort*factor;
Ch6_an[L]=Ch6_ort*factor;

}//fxの繰り返しに対応

fstream out00an("an_Legngrepoly.csv",ios::out|ios::binary |ios::app);

out00an<<"p_"<<"L"<<","<<"div"<<","<<"tr_an"<<","<<"s3_an"<<","<<"s8_an"<<","<<"b2_an"<<","
        <<"Le2_an"<<","<<"Le3_an"<<","<<"Le4_an"<<","<<"Le5_an"<<","<<"Le6_an"<<","<<"Ch2_an"<<","
        <<"Ch3_an"<<","<<"Ch4_an"<<","<<"Ch5_an"<<","<<"Ch6_an"<<endl;

for(int L=ak;L>=0;L--) out00an<<"p_"<<L<<","<<div<<","<<setprecision(20)<<tr_an[L]<<","<<s3_an[L]<<","
        <<s8_an[L]<<","<<b2_an[L]<<","<<Le2_an[L]<<","<<Le3_an[L]<<","<<Le4_an[L]<<","<<Le5_an[L]<<","
        <<Le6_an[L]<<","<<Ch2_an[L]<<","<<Ch3_an[L]<<","<<Ch4_an[L]<<","<<Ch5_an[L]<<","<<Ch6_an[L]<<endl;

out00an<<" "<<endl;
out00an.close();

long double x=0.0;
int kk=300+1;

vector<long double>gx_value(kk,0.0);
for(int j=0;j<kk;j++)
{
        x=0.02*j-3.0;
        gx_value[j]=g_function(x,a,b);
}

vector<long double>re_Le6(kk,0.0);
vector<long double>re_Le5(kk,0.0);
vector<long double>re_Le4(kk,0.0);
vector<long double>re_Le3(kk,0.0);
vector<long double>re_Le2(kk,0.0);

vector<long double>re_Ch6(kk,0.0);
vector<long double>re_Ch5(kk,0.0);
vector<long double>re_Ch4(kk,0.0);
vector<long double>re_Ch3(kk,0.0);
vector<long double>re_Ch2(kk,0.0);

vector<long double>re_b2(kk,0.0);
vector<long double>re_s8(kk,0.0);
vector<long double>re_s3(kk,0.0);
vector<long double>re_tr(kk,0.0);


for(int j=0;j<kk;j++)
{
        x=0.02*j-3.0;
        long double Le6_sum=0.0,Le5_sum=0.0,Le4_sum=0.0,Le3_sum=0.0,Le2_sum=0.0;
        long double Ch6_sum=0.0,Ch5_sum=0.0,Ch4_sum=0.0,Ch3_sum=0.0,Ch2_sum=0.0;
        long double b2_sum=0.0,s8_sum=0.0,s3_sum=0.0,tr_sum=0.0;

        for(int L=ak;L>=0;L--)
    {
    fx.clear();
    int m=L;
    for(int i=L*(L+1)/2;i<m+L*(L+1)/2+1;i++) fx.push_back(hx[i]);
    fx.resize(fx.size());       
        for(int i=0;i<m+1;i++)
        {
         Le6_sum=Le6_sum+Le6_an[L]*fx[i]*pow(x,i);
         Le5_sum=Le5_sum+Le5_an[L]*fx[i]*pow(x,i);
         Le4_sum=Le4_sum+Le4_an[L]*fx[i]*pow(x,i);
         Le3_sum=Le3_sum+Le3_an[L]*fx[i]*pow(x,i);
         Le2_sum=Le2_sum+Le2_an[L]*fx[i]*pow(x,i);

         Ch6_sum=Ch6_sum+Ch6_an[L]*fx[i]*pow(x,i);
         Ch5_sum=Ch5_sum+Ch5_an[L]*fx[i]*pow(x,i);
         Ch4_sum=Ch4_sum+Ch4_an[L]*fx[i]*pow(x,i);
         Ch3_sum=Ch3_sum+Ch3_an[L]*fx[i]*pow(x,i);
         Ch2_sum=Ch2_sum+Ch2_an[L]*fx[i]*pow(x,i);

         b2_sum=b2_sum+b2_an[L]*fx[i]*pow(x,i);
         s8_sum=s8_sum+s8_an[L]*fx[i]*pow(x,i);
         s3_sum=s3_sum+s3_an[L]*fx[i]*pow(x,i);
         tr_sum=tr_sum+tr_an[L]*fx[i]*pow(x,i);

        }               
        }
        re_Le6[j]=Le6_sum;
        re_Le5[j]=Le5_sum;
        re_Le4[j]=Le4_sum;
        re_Le3[j]=Le3_sum;
        re_Le2[j]=Le2_sum;

        re_Ch6[j]=Ch6_sum;
        re_Ch5[j]=Ch5_sum;
        re_Ch4[j]=Ch4_sum;
        re_Ch3[j]=Ch3_sum;
        re_Ch2[j]=Ch2_sum;

        re_b2[j]=b2_sum;
        re_s8[j]=s8_sum;
        re_s3[j]=s3_sum;
        re_tr[j]=tr_sum;

}

fstream outrecalc("Re-calculation_result.csv",ios::out |ios::binary  |ios::app);

outrecalc<<"div"<<","<<"j"<<","<<"0.02*j-3.0"<<","<<"re_Le6"<<","<<"re_Le5"<<","<<"re_Le4"<<","
        <<"re_Le3"<<","<<"re_Le2"<<","<<"re_Ch6"<<","<<"re_Ch5"<<","<<"re_Ch4"<<","<<"re_Ch3"<<","
        <<"re_Ch2"<<","<<"re_b2"<<","<<"re_s8"<<","<<"re_s3"<<","<<"re_tr"<<","<<"gx_value"<<","
        <<"gx_value-re_Le6"<<endl;

for(int j=0;j<(int)re_Le6.size();j++) 
        outrecalc<<div<<","<<setw(3)<<j<<","<<0.02*j-3.0<<","<<setprecision(20)<<re_Le6[j]<<","<<re_Le5[j]
<<","<<re_Le4[j]<<","<<re_Le3[j]<<","<<re_Le2[j]<<","<<re_Ch6[j]<<","<<re_Ch5[j]<<","<<re_Ch4[j]<<","
        <<re_Ch3[j]<<","<<re_Ch2[j]<<","<<re_b2[j]<<","<<re_s8[j]<<","<<re_s3[j]<<","<<re_tr[j]<<","
        <<gx_value[j]<<","<<gx_value[j]-re_Le6[j]<<endl;


outrecalc<<" "<<endl;
outrecalc.close();

re_Le6.clear();
re_Le5.clear();
re_Le4.clear();
re_Le3.clear();
re_Le2.clear();

re_Ch6.clear();
re_Ch5.clear();
re_Ch4.clear();
re_Ch3.clear();
re_Ch2.clear();

re_b2.clear();
re_s8.clear();
re_s3.clear();
re_tr.clear();

}// div0[i]に対応

return 0;
}

vector<double> Legendre_function()
{
//Legendre関数p　
vector<double >p0(0+1,0.0);
p0[0]=1.0;

// 以下、コード　L-1 と同じ故に削除



// 以上　コード　L-1 と同じ故に、削除 

p34[33]=0.0;
p34[34]=7113260368810144185/4294967296.0;


int k;
vector<double>hx;
k=0;for(int i=0;i<k+1;i++)      hx.push_back(p0[i]);
k=1;for(int i=0;i<k+1;i++)      hx.push_back(p1[i]);

// 以下　繰り返し故に　削除


// 以上　繰り返し故に削除

k=34;for(int i=0;i<k+1;i++)     hx.push_back(p34[i]);
hx.resize(hx.size());

return hx;

}

本章 7章の説明へ


7、Legendre 多項式による級数展開　Bessel関数 J1/2(x)への適用 (コード D-3)
#include <cmath>
#include <fstream>
#include <vector>
#include <iomanip>
#include <numeric>
#include <iostream>
using namespace std;

const long double PI=3.14159265358979323846264338327950288;

vector<double> Legendre_function();

double g_function(double x,double a, double b) 
{
        if(x<=0.0) 
        {
                return 0.0;
        }
        else
        {
         return sqrt(2*PI*x/PI)*(sin(PI*x))/(PI*x);
        }
}

//Legendre多項式による多項式展開
int main()
{

vector<double>hx;
hx=Legendre_function();
hx.resize(hx.size());

double a=0.0;
double b=0.0;

//Gauss-Legendre
//2分点
double x20=-1.0/sqrt(3.0);
double x21=1.0/sqrt(3.0);
//重み係数
double wLe2_0=1.0;
double wLe2_1=1.0;

//　以下　次章に記載する　あるいは後日に記載する　ので　削除


// 以上　次章に記載する　あるいは　後日に記載する　ので　削除

// 6 分点　重み 1/3    
double xCh60=-0.86624681810782;
double xCh61=-0.422518653761111;
double xCh62=-0.266635401516705;
double xCh63=0.266635401516705;
double xCh64=0.422518653761111;
double xCh65=0.86624681810782;
double wCh6=1.0/3.0;


//区間分割数
vector<int>div0(2+1,0);
div0[0]=4000;
div0[1]=6300;
div0[2]=10000;


//a0,a1,..,anの係数用積分区間
double x0=0.0; // 積分域を x0=-1.0 から変更。奇関数と見なして。
double x1=1.0; 

for(int i=0;i<(int)div0.size();i++)
{
int div=div0[i];
vector<long double>fx;

int ak=29;//展開するLegendre関数の次数

//an値の格納部分
vector<long double>tr_an(ak+1,0.0),s3_an(ak+1,0.0);
vector<long double>s8_an(ak+1,0.0),b2_an(ak+1,0.0);
vector<long double>Le2_an(ak+1,0.0),Le3_an(ak+1,0.0);
vector<long double>Le4_an(ak+1,0.0),Le5_an(ak+1,0.0);
vector<long double>Le6_an(ak+1,0.0),Ch2_an(ak+1,0.0);
vector<long double>Ch3_an(ak+1,0.0),Ch4_an(ak+1,0.0);
vector<long double>Ch5_an(ak+1,0.0),Ch6_an(ak+1,0.0);

for(int L=ak;L>=0;L--)
{
fx.clear();
int m=L;
for(int i=L*(L+1)/2;i<m+L*(L+1)/2+1;i++) fx.push_back(hx[i]);
fx.resize(fx.size());

double factor=(2.0*L+1)/2.0;//Legendreの直交係数の逆数

double h=(x1-x0)/div;
double f_xn0=0.0;//分割始点
double f_xn2=0.0;//幅の1/4点
double f_xn3=0.0;//幅の1/3点
double f_xnm=0.0;//中間点
double f_xn6=0.0;//幅の2/3点
double f_xn7=0.0;//幅の3/4点
double f_xn1=0.0;//終点

double g_xn0=0.0;//分割始点
double g_xn2=0.0;//幅の1/4点
double g_xn3=0.0;//幅の1/3点
double g_xnm=0.0;//中間点
double g_xn6=0.0;//幅の2/3点
double g_xn7=0.0;//幅の3/4点
double g_xn1=0.0;//終点

double fg_xn0=0.0;
double fg_xnm=0.0;
double fg_xn1=0.0;

double tr_ort=0.0;// trapezoid 台形則
double s3_ort=0.0;// simpson　1/3則 
double s8_ort=0.0;// simpson　3/8則
double b2_ort=0.0;// Boole則 2/45

double Le2_ort=0.0;// Gauss-Legendre 2次 　
double Le3_ort=0.0;// Gauss-Legendre 3次
double Le4_ort=0.0;// Gauss-Legendre 4次
double Le5_ort=0.0;// Gauss-Legendre 5次
double Le6_ort=0.0;// Gauss-Legendre 6次

double Ch2_ort=0.0;// Chebyshev式 2次 
double Ch3_ort=0.0;// Chebyshev式 3次 
double Ch4_ort=0.0;// Chebyshev式 4次 
double Ch5_ort=0.0;// Chebyshev式 5次  
double Ch6_ort=0.0;// Chebyshev式 6次 


for(int j=0;j<div;j++)
{ 

 //台形則、simpson則、Boole則
 vector<double>p_xn0(m+1,0.0);
 vector<double>p_xn2(m+1,0.0);
 vector<double>p_xn3(m+1,0.0);
 vector<double>p_xnm(m+1,0.0);
 vector<double>p_xn6(m+1,0.0);
 vector<double>p_xn7(m+1,0.0);
 vector<double>p_xn1(m+1,0.0);
 
 

  for(int i=0;i<m+1;i++)
 {
         p_xn0[i]=pow(x0+j*h,i);
         p_xn2[i]=pow(x0+j*h+h/4.0,i);
     p_xn3[i]=pow(x0+j*h+h/3.0,i);
         p_xnm[i]=pow(x0+j*h+h/2.0,i);
         p_xn6[i]=pow(x0+j*h+2.0*h/3.0,i);
         p_xn7[i]=pow(x0+j*h+3.0*h/4.0,i);
     p_xn1[i]=pow(x0+j*h+h,i);
 }  
 f_xn0=inner_product(fx.begin(),fx.end(),p_xn0.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn2=inner_product(fx.begin(),fx.end(),p_xn2.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn3=inner_product(fx.begin(),fx.end(),p_xn3.begin(),0.0,plus<double>(),multiplies<double>());
 f_xnm=inner_product(fx.begin(),fx.end(),p_xnm.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn6=inner_product(fx.begin(),fx.end(),p_xn6.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn7=inner_product(fx.begin(),fx.end(),p_xn7.begin(),0.0,plus<double>(),multiplies<double>());
 f_xn1=inner_product(fx.begin(),fx.end(),p_xn1.begin(),0.0,plus<double>(),multiplies<double>());
 
 g_xn0=g_function(x0+j*h,a,b);
 g_xn2=g_function(x0+j*h+h/4.0,a,b);
 g_xn3=g_function(x0+j*h+h/3.0,a,b);
 g_xnm=g_function(x0+j*h+h/2.0,a,b);
 g_xn6=g_function(x0+j*h+2.0*h/3.0,a,b);
 g_xn7=g_function(x0+j*h+3.0*h/4.0,a,b);
 g_xn1=g_function(x0+j*h+h,a,b);

 fg_xn0=f_xn0*g_xn0;
 fg_xnm=f_xnm*g_xnm;
 fg_xn1=f_xn1*g_xn1;
 
 tr_ort=tr_ort+(fg_xn0+fg_xn1)*h/2.0;
 s3_ort=s3_ort+(fg_xn0+4.0*fg_xnm+fg_xn1)/3.0*h/2.0;  
 s8_ort=s8_ort+(fg_xn0+3.0*f_xn3*g_xn3+3.0*f_xn6*g_xn6+fg_xn1)*3.0/8.0*h/3.0;
 b2_ort=b2_ort+(7.0*fg_xn0+32.0*f_xn2*g_xn2+12.0*fg_xnm+32.0*f_xn7*g_xn7+7.0*fg_xn1)*2.0/45.0*h/4.0;  

//Gauss-Legendre
//2分点
double xLe2_0=x0+j*h+h/2.0+h/2.0*x20;
double xLe2_1=x0+j*h+h/2.0+h/2.0*x21;


double Le2_0=0.0,Le2_1=0.0;


for(int i=0;i<m+1;i++) 
 { 
  Le2_0=Le2_0+fx[i]*pow(xLe2_0,i);
  Le2_1=Le2_1+fx[i]*pow(xLe2_1,i); 
 }

double gLe2_0=0.0,gLe2_1=0.0;
gLe2_0=g_function(xLe2_0,a,b);
gLe2_1=g_function(xLe2_1,a,b); 

Le2_ort=Le2_ort+h/2.0*(wLe2_0*Le2_0*gLe2_0+wLe2_1*Le2_1*gLe2_1);


// 以下　次章に記載する　あるいは　後日に追加する　ので　削除

// 以上 次章に記載する　あるいは　後日に追加する　ので　削除

gCh6_1=g_function(xCh6_1,a,b);
gCh6_2=g_function(xCh6_2,a,b);
gCh6_3=g_function(xCh6_3,a,b);
gCh6_4=g_function(xCh6_4,a,b);
gCh6_5=g_function(xCh6_5,a,b);

Ch6_ort=Ch6_ort+h/2.0*wCh6*(Ch6_0*gCh6_0+Ch6_1*gCh6_1+Ch6_2*gCh6_2+Ch6_3*gCh6_3+Ch6_4*gCh6_4+Ch6_5*gCh6_5);

}//div



cout<<"p_"<<L<<","<<div<<endl;

tr_an[L]=tr_ort*factor;
s3_an[L]=s3_ort*factor;  
s8_an[L]=s8_ort*factor;
b2_an[L]=b2_ort*factor;
Le2_an[L]=Le2_ort*factor;
Le3_an[L]=Le3_ort*factor;
Le4_an[L]=Le4_ort*factor;
Le5_an[L]=Le5_ort*factor;
Le6_an[L]=Le6_ort*factor;
Ch2_an[L]=Ch2_ort*factor;
Ch3_an[L]=Ch3_ort*factor;
Ch4_an[L]=Ch4_ort*factor;
Ch5_an[L]=Ch5_ort*factor;
Ch6_an[L]=Ch6_ort*factor;

}//fxの繰り返しに対応

fstream out00an("an_Legngrepoly.csv",ios::out|ios::binary |ios::app);
out00an<<"p_"<<"L"<<","<<"div"<<","<<"tr_an"<<","<<"s3_an"<<","<<"s8_an"<<","<<"b2_an"<<","
        <<"Le2_an"<<","<<"Le3_an"<<","<<"Le4_an"<<","<<"Le5_an"<<","<<"Le6_an"<<","<<"Ch2_an"<<","
        <<"Ch3_an"<<","<<"Ch4_an"<<","<<"Ch5_an"<<","<<"Ch6_an"<<endl;

for(int L=ak;L>=0;L--) out00an<<"p_"<<L<<","<<div<<","<<setprecision(20)<<tr_an[L]<<","<<s3_an[L]<<","
        <<s8_an[L]<<","<<b2_an[L]<<","<<Le2_an[L]<<","<<Le3_an[L]<<","<<Le4_an[L]<<","<<Le5_an[L]<<","
        <<Le6_an[L]<<","<<Ch2_an[L]<<","<<Ch3_an[L]<<","<<Ch4_an[L]<<","<<Ch5_an[L]<<","<<Ch6_an[L]<<endl;

out00an<<" "<<endl;
out00an.close();

long double x=0.0;
int kk=1000+1;

vector<long double>gx_value(kk,0.0);
for(int j=0;j<kk;j++)
{
        x=0.001*j;
        gx_value[j]=g_function(x,a,b);
}

vector<long double>re_Le6(kk,0.0);
vector<long double>re_Le5(kk,0.0);
vector<long double>re_Le4(kk,0.0);
vector<long double>re_Le3(kk,0.0);
vector<long double>re_Le2(kk,0.0);

vector<long double>re_Ch6(kk,0.0);
vector<long double>re_Ch5(kk,0.0);
vector<long double>re_Ch4(kk,0.0);
vector<long double>re_Ch3(kk,0.0);
vector<long double>re_Ch2(kk,0.0);

vector<long double>re_b2(kk,0.0);
vector<long double>re_s8(kk,0.0);
vector<long double>re_s3(kk,0.0);
vector<long double>re_tr(kk,0.0);


for(int j=0;j<kk;j++)
{
        x=0.001*j;

        long double Le6_sum=0.0,Le5_sum=0.0,Le4_sum=0.0,Le3_sum=0.0,Le2_sum=0.0;
        long double Ch6_sum=0.0,Ch5_sum=0.0,Ch4_sum=0.0,Ch3_sum=0.0,Ch2_sum=0.0;
        long double b2_sum=0.0,s8_sum=0.0,s3_sum=0.0,tr_sum=0.0;

        for(int L=ak;L>=0;L--)
    {
    fx.clear();
    int m=L;
    for(int i=L*(L+1)/2;i<m+L*(L+1)/2+1;i++) fx.push_back(hx[i]);
    fx.resize(fx.size());       
        for(int i=0;i<m+1;i++)
        {
         Le6_sum=Le6_sum+Le6_an[L]*fx[i]*pow(x,i);
         Le5_sum=Le5_sum+Le5_an[L]*fx[i]*pow(x,i);
         Le4_sum=Le4_sum+Le4_an[L]*fx[i]*pow(x,i);
         Le3_sum=Le3_sum+Le3_an[L]*fx[i]*pow(x,i);
         Le2_sum=Le2_sum+Le2_an[L]*fx[i]*pow(x,i);

         Ch6_sum=Ch6_sum+Ch6_an[L]*fx[i]*pow(x,i);
         Ch5_sum=Ch5_sum+Ch5_an[L]*fx[i]*pow(x,i);
         Ch4_sum=Ch4_sum+Ch4_an[L]*fx[i]*pow(x,i);
         Ch3_sum=Ch3_sum+Ch3_an[L]*fx[i]*pow(x,i);
         Ch2_sum=Ch2_sum+Ch2_an[L]*fx[i]*pow(x,i);

         b2_sum=b2_sum+b2_an[L]*fx[i]*pow(x,i);
         s8_sum=s8_sum+s8_an[L]*fx[i]*pow(x,i);
         s3_sum=s3_sum+s3_an[L]*fx[i]*pow(x,i);
         tr_sum=tr_sum+tr_an[L]*fx[i]*pow(x,i);

        }               
        }
        re_Le6[j]=Le6_sum;
        re_Le5[j]=Le5_sum;
        re_Le4[j]=Le4_sum;
        re_Le3[j]=Le3_sum;
        re_Le2[j]=Le2_sum;

        re_Ch6[j]=Ch6_sum;
        re_Ch5[j]=Ch5_sum;
        re_Ch4[j]=Ch4_sum;
        re_Ch3[j]=Ch3_sum;
        re_Ch2[j]=Ch2_sum;

        re_b2[j]=b2_sum;
        re_s8[j]=s8_sum;
        re_s3[j]=s3_sum;
        re_tr[j]=tr_sum;

}

fstream outrecalc("Re-calculation_result.csv",ios::out |ios::binary  |ios::app);

outrecalc<<"div"<<","<<"j"<<","<<"0.001*j"<<","<<"re_Le6"<<","<<"re_Le5"<<","<<"re_Le4"<<","
        <<"re_Le3"<<","<<"re_Le2"<<","<<"re_Ch6"<<","<<"re_Ch5"<<","<<"re_Ch4"<<","<<"re_Ch3"<<","
        <<"re_Ch2"<<","<<"re_b2"<<","<<"re_s8"<<","<<"re_s3"<<","<<"re_tr"<<","<<"gx_value"<<","
        <<"gx_value-re_Le6"<<endl;

for(int j=0;j<(int)re_Le6.size();j++) 
        outrecalc<<div<<","<<setw(3)<<j<<","<<0.001*j<<","<<setprecision(20)<<re_Le6[j]<<","<<re_Le5[j]
<<","<<re_Le4[j]<<","<<re_Le3[j]<<","<<re_Le2[j]<<","<<re_Ch6[j]<<","<<re_Ch5[j]<<","<<re_Ch4[j]<<","
        <<re_Ch3[j]<<","<<re_Ch2[j]<<","<<re_b2[j]<<","<<re_s8[j]<<","<<re_s3[j]<<","<<re_tr[j]<<","
        <<gx_value[j]<<","<<gx_value[j]-re_Le6[j]<<endl;

outrecalc<<" "<<endl;
outrecalc.close();

re_Le6.clear();
re_Le5.clear();
re_Le4.clear();
re_Le3.clear();
re_Le2.clear();

re_Ch6.clear();
re_Ch5.clear();
re_Ch4.clear();
re_Ch3.clear();
re_Ch2.clear();

re_b2.clear();
re_s8.clear();
re_s3.clear();
re_tr.clear();

}// div0[i]に対応

return 0;
}

vector<double> Legendre_function()
{
//Legendre関数p　
vector<double >p0(0+1,0.0);
p0[0]=1.0;

// 以下、コード　L-1 と同じ故に削除


// 以上　コード　L-1 と同じ故に、削除 

p34[33]=0.0;
p34[34]=7113260368810144185/4294967296.0;


int k;
vector<double>hx;
k=0;for(int i=0;i<k+1;i++)      hx.push_back(p0[i]);
k=1;for(int i=0;i<k+1;i++)      hx.push_back(p1[i]);

// 以下　繰り返し故に　削除


// 以上　繰り返し故に削除

k=34;for(int i=0;i<k+1;i++)     hx.push_back(p34[i]);
hx.resize(hx.size());

return hx;

}

本章 7章の説明へ

8、Bessel 関数の図

#include <cmath>
#include <fstream>
#include <iomanip>
#include <numeric>
#include <iostream>
using namespace std;
 
const double PI=3.14159265358979323846264338327950288;
 
int main()
{
 
fstream outbessel("J0_1_2andJ7and5and3and1andminus.csv",ios::out |ios::binary |ios::app);
outbessel<<"x"<<","<<"J-1/2"<<","<<"J1/2"<<","<<"J3/2"<<","<<"J5/2"<<","<<"J7/2"<<","<<"J0"<<","<<"J1"<<","<<"J2"<<endl;
 
for(int n=0;n<200;n++)
{
 
double x=4.0*PI*(n+1)/200.0;
 
double J0_72=1.0-(x/2.0)*(x/2.0)+(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/4.0
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(3.0*2.0)/(3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(4.0*3.0*2.0)/(4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(5.0*4.0*3.0*2.0)/(5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(6.0*5.0*4.0*3.0*2.0)
 /(6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(7.0*6.0*5.0*4.0*3.0*2.0)/(7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)/(8.0*7.0*6.0*5.0*4.0*3.0*2.0)/(8.0*7.0*6.0*5.0*4.0*3.0*2.0)-(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)/(9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)/(10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 /(11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 /(12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)-(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)/(13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)/(13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(14.0*13.0*12.0
 *11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)/(14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 /(15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)/(16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)/(16.0*15.0*14.0*13.0*12.0*11.0*10.0
 *9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 /(17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0
 *3.0*2.0)/(18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0
 *8.0*7.0*6.0*5.0*4.0*3.0*2.0)/(19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0
 *12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 /(20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(21.0*20.0*19.0*18.0
 *17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 /(21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 /(22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)/(23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 /(23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)
 /(24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 /(24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 /(25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 /(26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0
 *18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)/(27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0
 *19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(28.0*27.0*26.0*25.0*24.0*23.0
 *22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)/(28.0*27.0*26.0*25.0
 *24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(29.0*28.0*27.0
 *26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 /(29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0
 *5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0
 *6.0*5.0*4.0*3.0*2.0)/(30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0
 *11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)/(31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0
 *11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)/(31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0
 *16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0
 *15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)/(32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0
 *21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0
 *19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)/(33.0*32.0*31.0*30.0*29.0*28.0*27.0
 *26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(34.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0
 *23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)/(34.0*33.0*32.0
 *31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0
 *7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(35.0*34.0*33.0*32.0*31.0*30.0*29.0
 *28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0
 *3.0*2.0)/(35.0*34.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0
 *14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(36.0*35.0*34.0*33.0
 *32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0
 *8.0*7.0*6.0*5.0*4.0*3.0*2.0)/(36.0*35.0*34.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0
 *19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0);
 
 
double J1_73=(x/2.0)-(x/2.0)*(x/2.0)*(x/2.0)/2.0+(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(2.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(3.0*2.0*4.0*3.0*2.0)+(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(4.0*3.0*2.0*5.0*4.0*3.0*2.0)-(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(5.0*4.0*3.0*2.0*6.0*5.0*4.0*3.0*2.0)+(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(6.0*5.0*4.0*3.0*2.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(7.0*6.0*5.0*4.0*3.0*2.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)/(8.0*7.0*6.0*5.0*4.0*3.0*2.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)/(15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0
 *16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)/(16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*17.0*16.0*15.0*14.0*13.0
 *12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*18.0
 *17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0
 *5.0*4.0*3.0*2.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0
 *10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(20.0*19.0*18.0*17.0*16.0*15.0
 *14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0
 *10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0
 *22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0
 *23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)/(23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0
 *24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0
 *6.0*5.0*4.0*3.0*2.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0
 *14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0
 *11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0
 *16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0
 *16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0
 *17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(27.0*26.0*25.0*24.0*23.0*22.0*21.0
 *20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*28.0*27.0*26.0*25.0*24.0*23.0
 *22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(28.0*27.0*26.0*25.0
 *24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*29.0*28.0
 *27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(29.0
 *28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0
 *3.0*2.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0
 *10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)/(30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0
 *8.0*7.0*6.0*5.0*4.0*3.0*2.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0
 *13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)/(31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0
 *14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0
 *20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0
 *17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0
 *24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0
 *21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*34.0*33.0*32.0*31.0*30.0
 *29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0
 *11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(34.0*33.0*32.0*31.0*30.0*29.0*28.0
 *27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0
 *5.0*4.0*3.0*2.0*35.0*34.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0
 *17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(35.0*34.0*33.0*32.0
 *31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0
 *9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*36.0*35.0*34.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0
 *20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(36.0*35.0
 *34.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0
 *11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*37.0*36.0*35.0*34.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0
 *22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0);
 
 
double J2_72= (x/2.0)*(x/2.0)/2.0
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(3.0*2.0)+(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(2.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(3.0*2.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(4.0*3.0*2.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(5.0*4.0*3.0*2.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(6.0*5.0*4.0*3.0*2.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)/(7.0*6.0*5.0*4.0*3.0*2.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)/(8.0*7.0*6.0*5.0*4.0*3.0*2.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(12.0*11.0*10.0*9.0*8.0*7.0
 *6.0*5.0*4.0*3.0*2.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)/(15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*17.0*16.0*15.0*14.0*13.0*12.0
 *11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*18.0*170.*16.0
 *15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0
 *3.0*2.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0
 *8.0*7.0*6.0*5.0*4.0*3.0*2.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(19.0*18.0*17.0*16.0*15.0*14.0*13.0
 *12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0
 *14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(20.0*19.0*18.0*17.0
 *16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0
 *14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*23.0*22.0*21.0*20.0*19.0
 *18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)/(22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*24.0*23.0
 *22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)/(23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0
 *4.0*3.0*2.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0
 *9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0
 *15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0
 *13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0
 *15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0
 *18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0
 *20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(27.0*26.0*25.0*24.0*23.0
 *22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*29.0*28.0*27.0
 *26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(28.0*27.0
 *26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0
 *30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0
 *12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 /(29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0
 *5.0*4.0*3.0*2.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0
 *13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)/(30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0
 *10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0
 *16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0
 *14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0
 *21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0
 *18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*34.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0
 *26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0
 *23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*35.0*34.0*33.0
 *32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0
 *13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 +(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(34.0*33.0*32.0*31.0*30.0*29.0*28.0
 *27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0
 *2.0*36.0*35.0*34.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0
 *16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
 -(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)
 *(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(35.0*34.0*33.0*32.0
 *31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0
 *7.0*6.0*5.0*4.0*3.0*2.0*37.0*36.0*35.0*34.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0
 *19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0);
 
 
double Jminus1by2=sqrt(2.0/PI/x)*(cos(x));
double J1by2=sqrt(2/PI/x)*sin(x);
double J3by2=sqrt(2/PI/x)*(sin(x)/x-cos(x));
double J5by2=sqrt(2/PI/x)*((3.0/x/x-1)*sin(x)-3.0*cos(x)/x);
double J7by2=sqrt(2.0/PI/x)*((-6.0/x+15.0/(x*x*x))*sin(x)+(1.0-15.0/(x*x))*cos(x));
 
outbessel<<setprecision(25)<<x<<","<<Jminus1by2<<","<<J1by2<<","<<J3by2<<","<<J5by2<<","<<J7by2<<","<<J0_72<<","<<J1_73<<","<<J2_72<<endl;
 
}
outbessel.close();
 
 
return 0;
}
 
 

本章 7章の説明へ


9、不等間隔の積分によるBessl 関数の算出

#include <fstream>
#include <vector>
#include <iomanip>
#include <numeric>
using namespace std;

double J0_72(double x);
double J1_73(double x);
double J2_72(double x);

double J1by2(double x);
double J3by2(double x);
double J5by2(double x);
double J7by2(double x);

double Jminus1by2(double x);
double Jminus3by2(double x);
double Jminus5by2(double x);

const double PI=3.14159265358979323846264338327950288;


//不等間隔の積分
int main()
{
// 不等間隔データ算出

double p=0;
int kdiv=400;
int m=0;
double x=0.0;
vector<double>x_axis(kdiv+1,0.0);

for(int j=0;j<=kdiv;j++)
{

p=0.75*(double)j*j+p;
x_axis[j]=2.0*PI/kdiv*(p+j);
if(x_axis[j]>2.0*PI) { m=j; break;}
}
x_axis[m]=2.0*PI;
x_axis.resize(m+1);

fstream outxaxis("x_axis.csv",ios::out |ios::binary );
outxaxis<<"j"<<","<<"x_axis[j]"<<","<<"x_axis[j]-x_axis[j-1]"<<endl;
outxaxis<<0<<","<<x_axis[0]<<endl;
for(int j=1;j<(int)x_axis.size();j++){setw(30); outxaxis<<setprecision(25)<<j<<","<<x_axis[j]<<","<<x_axis[j]-x_axis[j-1]<<endl;}
// j-1があるので、j=1から始まる
outxaxis.close();

// 積分計算用　data

double xx=0.0;

vector<double>J0_y(x_axis.size(),0.0);
vector<double>J1_y(x_axis.size(),0.0);
vector<double>J2_y(x_axis.size(),0.0);

vector<double>J1by2_y(x_axis.size(),0.0);
vector<double>J3by2_y(x_axis.size(),0.0);
vector<double>J5by2_y(x_axis.size(),0.0);
vector<double>J7by2_y(x_axis.size(),0.0);

vector<double>Jminus1by2_y(x_axis.size(),0.0);
vector<double>Jminus3by2_y(x_axis.size(),0.0);
vector<double>Jminus5by2_y(x_axis.size(),0.0);

vector<double>dJ0_y(x_axis.size(),0.0);
vector<double>dJ1_y(x_axis.size(),0.0);

vector<double>dJ1by2_y(x_axis.size(),0.0);
vector<double>dJ3by2_y(x_axis.size(),0.0);
vector<double>dJ5by2_y(x_axis.size(),0.0);

vector<double>dJminus1by2_y(x_axis.size(),0.0);
vector<double>dJminus3by2_y(x_axis.size(),0.0);

for(int j=0;j<(int)x_axis.size();j++)
{
xx=x_axis[j];

dJ0_y[j]=-J1_73(xx);
dJ1_y[j]=-J2_72(xx)/2.0+J0_72(xx)/2.0;

dJ1by2_y[j]=-J3by2(xx)/2.0+Jminus1by2(xx)/2.0;
dJ3by2_y[j]=-J5by2(xx)/2.0+J1by2(xx)/2.0;
dJ5by2_y[j]=-J7by2(xx)/2.0+J3by2(xx)/2.0;

dJminus1by2_y[j]=-J1by2(xx)/2.0+Jminus3by2(xx)/2.0;
dJminus3by2_y[j]=-Jminus1by2(xx)/2.0+Jminus5by2(xx)/2.0;

J0_y[j]=J0_72(xx);
J1_y[j]=J1_73(xx);
J2_y[j]=J2_72(xx);

J1by2_y[j]=J1by2(xx);
J3by2_y[j]=J3by2(xx);
J5by2_y[j]=J5by2(xx);
J7by2_y[j]=J7by2(xx);

Jminus5by2_y[j]=Jminus5by2(xx);
Jminus3by2_y[j]=Jminus3by2(xx);
Jminus1by2_y[j]=Jminus1by2(xx);

}

fstream out1("Jminus5by2_to_J2.csv",ios::out |ios::binary );
out1<<"j"<<","<<"x_axis[j]"<<","<<"Jminus5by2[j]"<<","<<"Jminus3by2[j]"<<","<<"Jminus1by2[j]"<<","<<"J1by2[j]"<<","<<"J3by2[j]"<<","
<<"J5by2[j]"<<","<<"J7by2"<<","<<"J0[j]"<<","<<"J1[j]"<<","<<"J2[j]"<<endl;
for(int j=0;j<(int)x_axis.size();j++){setw(30); out1<<setprecision(25)<<j<<","<<x_axis[j]<<","<<Jminus5by2_y[j]<<","
<<Jminus3by2_y[j]<<","<<Jminus1by2_y[j]<<","<<J1by2_y[j]<<","<<J3by2_y[j]<<","<<J5by2_y[j]
<<","<<J7by2_y[j]<<","<<J0_y[j]<<","<<J1_y[j]<<","<<J2_y[j]<<endl;}
out1.close();

fstream out2("dJminus3by2_to_dJ1.csv",ios::out |ios::binary );
out2<<"j"<<","<<"x_axis[j]"<<","<<"dJminus3by2[j]"<<","<<"dJminus1by2[j]"<<","<<"dJ1by2[j]"<<","<<"dJ3/2[j]"<<","
<<"dJ5/2[j]"<<","<<"dJ0"<<","<<"dJ1"<<endl;
for(int j=0;j<(int)x_axis.size();j++){ out2<<setprecision(25)<<j<<","<<x_axis[j]<<","<<dJminus3by2_y[j]<<","<<dJminus1by2_y[j]<<","<<dJ1by2_y[j]<<","
<<dJ3by2_y[j]<<","<<dJ5by2_y[j]<<","<<dJ0_y[j]<<","<<dJ1_y[j]<<endl;}
out2.close();


vector<double>y_value(7*(int)x_axis.size(),0.0);
for(int j=0;j<(int)x_axis.size();j++) {y_value[j]=dJ1by2_y[j],y_value[j+1*(int)x_axis.size()]=dJ3by2_y[j],
y_value[j+2*(int)x_axis.size()]=dJ5by2_y[j]
,y_value[j+3*(int)x_axis.size()]=dJ0_y[j],
y_value[j+4*(int)x_axis.size()]=dJ1_y[j],y_value[j+5*(int)x_axis.size()]=dJminus1by2_y[j],y_value[j+6*(int)x_axis.size()]=dJminus3by2_y[j];}

fstream out3("y_value.csv",ios::out |ios::binary );
out3<<"j"<<","<<"x_axis[j]"<<","<<"dJ1by2[j]"<<","<<"dJ3/2[j]"<<","<<"dJ5/2[j]"<<","<<"dJ0"<<","<<"dJ1"<<","<<"dJminus1by2"
<<","<<"dJminus3by2"<<endl;
for(int j=0;j<(int)x_axis.size();j++){out3<<setprecision(25)<<j<<","<<x_axis[j]<<","<<y_value[j]<<","<<y_value[j+1*(int)x_axis.size()]<<","
<<y_value[j+2*(int)x_axis.size()]<<","<<y_value[j+3*(int)x_axis.size()]
<<","<<y_value[j+4*(int)x_axis.size()]<<","<<y_value[j+5*(int)x_axis.size()]<<","<<y_value[j+6*(int)x_axis.size()]<<endl;}
out3.close();

vector<double>reffer_y(7*(int)x_axis.size(),0.0);
for(int j=0;j<(int)x_axis.size();j++) {reffer_y[j]=J1by2_y[j],reffer_y[j+(int)x_axis.size()]=J3by2_y[j],reffer_y[j+2*(int)x_axis.size()]=J5by2_y[j]
,reffer_y[j+3*(int)x_axis.size()]=J0_y[j],reffer_y[j+4*(int)x_axis.size()]=J1_y[j],reffer_y[j+5*(int)x_axis.size()]=Jminus1by2_y[j],
reffer_y[j+6*(int)x_axis.size()]=Jminus3by2_y[j];}

fstream out4("reffer_y.csv",ios::out |ios::binary );
out4<<"j"<<","<<"x_axis[j]"<<","<<"J1by2[j]"<<","<<"J3/2[j]"<<","<<"J5/2[j]"<<","<<"J0"<<","<<"J1"<<","<<"Jminus1/2"<<
","<<"Jminus3/2"<<endl;
for(int j=0;j<(int)x_axis.size();j++){out4<<setprecision(25)<<j<<","<<x_axis[j]<<","<<reffer_y[j]<<","<<reffer_y[j+1*(int)x_axis.size()]<<
","<<reffer_y[j+2*(int)x_axis.size()]<<","
<<reffer_y[j+3*(int)x_axis.size()]<<","<<reffer_y[j+4*(int)x_axis.size()]<<","<<reffer_y[j+5*(int)x_axis.size()]<<","
<<reffer_y[j+6*(int)x_axis.size()]<<endl;}
out4.close();


//不等間隔の積分

int k=6;

vector<double>start_y(7,0.0);
vector<double>final_y(7,0.0);
vector<double>refference(7,0.0);

double x0=x_axis[0+k];
double x1=x_axis[1+k];
double x2=x_axis[2+k];
double x3=x_axis[3+k];
double x4=x_axis[4+k];
double x5=x_axis[5+k];
double x6=x_axis[6+k];

vector<double>result(7,0.0);

// 2次積分式
double y20=0.0;
double y21=0.0;
double y22=0.0;

for(int n=0;n<7;n++)
{

y20=y_value[0+k+n*(int)x_axis.size()];
y21=y_value[1+k+n*(int)x_axis.size()];
y22=y_value[2+k+n*(int)x_axis.size()];

result[n]=
+(x2-x0)/(x1-x0)*(3.0*(x1-x0)-(x2-x0))/6.0*y20
+(x2-x0)*(x2-x0)*(x2-x0)/(x2-x1)/(x1-x0)/6.0*y21
+(x2-x0)/(x2-x1)*(3.0*(x2-x1)-(x2-x0))/6.0*y22
;

start_y[n]=reffer_y[0+k+n*(int)x_axis.size()];
final_y[n]=reffer_y[2+k+n*(int)x_axis.size()];
refference[n]=reffer_y[2+k+n*(int)x_axis.size()]-reffer_y[0+k+n*(int)x_axis.size()];

}

fstream out5("result_2_order.csv",ios::out |ios::binary );
out5<<" 不等間隔の 2 次積分式の結果　"<<endl;
out5<<" b = "<<","<<x2<<","<<" a= "<<","<<x0<<endl;
out5<<" 項目 "<<","<<"dJ1by2"<<","<<"dJ3/2"<<","<<"dJ5/2"<<","<<"dJ0"<<","<<"dJ1"<<","<<"dJminus1/2"<<","<<"dJminus3/2"<<endl;
out5<<" 積分結果 "<<","<<result[0]<<","<<result[1]<<","<<result[2]<<","<<result[3]<<","<<result[4]<<","<<result[5]<<","
<<result[6]<<endl;
out5<<" f(b)-f(a) "<<","<<refference[0]<<","<<refference[1]<<","<<refference[2]<<","<<refference[3]<<","<<refference[4]<<","<<refference[5]<<","
<<refference[6]<<endl;
out5<<" 誤差(%) "<<","<<(result[0]-refference[0])*100/refference[0]<<","<<(result[1]-refference[1])*100/refference[1]<<","<<(result[2]-refference[2])
*100/refference[2]<<","<<(result[3]-refference[3])*100/refference[3]<<","<<(result[4]-refference[4])*100/refference[4]<<","
<<(result[5]-refference[5])*100/refference[5]<<","<<(result[6]-refference[6])*100/refference[6]<<endl;
out5<<" f(b) "<<","<<final_y[0]<<","<<final_y[1]<<","<<final_y[2]<<","<<final_y[3]<<","<<final_y[4]<<","<<final_y[5]<<","
<<final_y[6]<<endl;
out5<<" f(a) "<<","<<start_y[0]<<","<<start_y[1]<<","<<start_y[2]<<","<<start_y[3]<<","<<start_y[4]<<","<<start_y[5]<<","<<start_y[6]<<endl;
out5.close();


// 3次積分式
double y30=0.0;
double y31=0.0;
double y32=0.0;
double y33=0.0;

for(int n=0;n<7;n++)
{

y30=y_value[0+k+n*(int)x_axis.size()];
y31=y_value[1+k+n*(int)x_axis.size()];
y32=y_value[2+k+n*(int)x_axis.size()];
y33=y_value[3+k+n*(int)x_axis.size()];

result[n]=
+1.0/12.0*(x3-x0)*(x3*x3-2.0*x3*x1-2.0*x3*x2+2.0*x0*x3+6.0*x1*x2-4.0*x0*x1-4.0*x0*x2+3.0*x0*x0)/(x2-x0)/(x1-x0)*y30
+1.0/12.0*(x3-x0)*(x3-x0)*(x3-x0)*(-x3-x0+2.0*x2)/(x1-x0)/(x2-x1)/(x3-x1)*y31
-1.0/12.0*(x3-x0)*(x3-x0)*(x3-x0)*(-x3+2.0*x1-x0)/(x2-x1)/(x2-x0)/(x3-x2)*y32
+1.0/12.0*(x3-x0)*(3.0*x3*x3-4.0*x3*x1-4.0*x3*x2+2.0*x0*x3+x0*x0-2.0*x1*x0-2.0*x2*x0+6.0*x1*x2)/(x3-x2)/(x3-x1)*y33
;

start_y[n]=reffer_y[0+k+n*(int)x_axis.size()];
final_y[n]=reffer_y[3+k+n*(int)x_axis.size()];
refference[n]=reffer_y[3+k+n*(int)x_axis.size()]-reffer_y[0+k+n*(int)x_axis.size()];

}

fstream out6("result_3_order.csv",ios::out |ios::binary );
out6<<" 不等間隔の 3 次積分式の結果　"<<endl;
out6<<" b = "<<","<<x3<<","<<" a= "<<","<<x0<<endl;
out6<<" 項目 "<<","<<"dJ1by2"<<","<<"dJ3/2"<<","<<"dJ5/2"<<","<<"dJ0"<<","<<"dJ1"<<","<<"dJminus1/2"<<","<<"dJminus3/2"<<endl;
out6<<" 積分結果 "<<","<<result[0]<<","<<result[1]<<","<<result[2]<<","<<result[3]<<","<<result[4]<<","<<result[5]<<","
<<result[6]<<endl;
out6<<" f(b)-f(a) "<<","<<refference[0]<<","<<refference[1]<<","<<refference[2]<<","<<refference[3]<<","<<refference[4]<<","<<refference[5]<<","
<<refference[6]<<endl;
out6<<" 誤差(%) "<<","<<(result[0]-refference[0])*100/refference[0]<<","<<(result[1]-refference[1])*100/refference[1]<<","<<(result[2]-refference[2])
*100/refference[2]<<","<<(result[3]-refference[3])*100/refference[3]<<","<<(result[4]-refference[4])*100/refference[4]<<","
<<(result[5]-refference[5])*100/refference[5]<<","<<(result[6]-refference[6])*100/refference[6]<<endl;
out6<<" f(b) "<<","<<final_y[0]<<","<<final_y[1]<<","<<final_y[2]<<","<<final_y[3]<<","<<final_y[4]<<","<<final_y[5]<<","
<<final_y[6]<<endl;
out6<<" f(a) "<<","<<start_y[0]<<","<<start_y[1]<<","<<start_y[2]<<","<<start_y[3]<<","<<start_y[4]<<","<<start_y[5]<<","<<start_y[6]<<endl;
out6.close();



return 0;
}

double J1by2(double x) { return sqrt(2.0/PI/x)*(sin(x));}
double J3by2(double x) { return sqrt(2.0/PI/x)*(sin(x)/x-cos(x));}
double J5by2(double x) { return sqrt(2.0/PI/x)*((3.0/(x*x)-1.0)*sin(x)-3.0*cos(x)/x);}
double J7by2(double x) { return sqrt(2.0/PI/x)*((-6.0/x+15.0/(x*x*x))*sin(x)+(1.0-15.0/(x*x))*cos(x));}

double Jminus1by2(double x) { return sqrt(2.0/PI/x)*(cos(x));}
double Jminus3by2(double x) { return sqrt(2.0/PI/x)*(-sin(x)-(cos(x))/x);}
double Jminus5by2(double x) { return sqrt(2.0/PI/x)*(3.0/x*sin(x)+(3.0/x/x-1.0)*cos(x));}

double J0_72(double x) { return 1.0-(x/2.0)*(x/2.0)+(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/4.0-(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(3.0*2.0)/(3.0*2.0)
---
---
/(36.0*35.0*34.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0
*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
;}

double J1_73(double x) { return
(x/2.0)-(x/2.0)*(x/2.0)*(x/2.0)/2.0+(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(2.0*3.0*2.0)

---
---

/(36.0*35.0*34.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0
*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*37.0*36.0*35.0*34.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0
*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)

;}



double J2_72(double x) { return (x/2.0)*(x/2.0)/2.0
-(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(3.0*2.0)
+(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)*(x/2.0)/(2.0*4.0*3.0*2.0)

---
---

/(35.0*34.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0
*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0*37.0*36.0*35.0*34.0*33.0*32.0*31.0*30.0*29.0*28.0*27.0*26.0*25.0*24.0*23.0*22.0*21.0*20.0
*19.0*18.0*17.0*16.0*15.0*14.0*13.0*12.0*11.0*10.0*9.0*8.0*7.0*6.0*5.0*4.0*3.0*2.0)
;}

本章 7章の説明へ


10、Chebyshev 多項式による級数展開 (コード E-1 )

#include <cmath>
#include <fstream>
#include <vector>
#include <iomanip>
#include <numeric>
#include <iostream>
using namespace std;

const long double PI=3.14159265358979323846264338327950288;

vector<double> Chebyshev_function();

//Chebyshev 多項式による多項式展開
int main()
{

vector<double>hx;
hx=Chebyshev_function();
hx.resize(hx.size());

//Chebyshev多項式展開を行う被対象の11次 Legendre関数
vector<double>p11(11+1,0.0);
p11[0]=0.0;
p11[1]=-693/256.0;
p11[2]=0.0;
p11[3]=15015/256.0;
p11[4]=0.0;
p11[5]=-45045/128.0;
p11[6]=0.0;
p11[7]=109395/128.0;
p11[8]=0.0;
p11[9]=-230945/256.0;
p11[10]=0.0;
p11[11]=88179/256.0;

vector<double>gx;
gx=p11;
gx.resize(gx.size());
int n=(int)gx.size();//被対象関数の次数

//Gauss-Legendre
// 6分点　分点
double x60=-0.93246951420315;
double x61=-0.661209386466265;
double x62=-0.238619186083197;
double x63=0.238619186083197;
double x64=0.661209386466265;
double x65=0.93246951420315;
//重み係数
double wLe6_0=0.171324492379176;
double wLe6_1=0.360761573048438;
double wLe6_2=0.467913934572691;
double wLe6_3=0.467913934572691;
double wLe6_4=0.360761573048438;
double wLe6_5=0.171324492379176;


//区間分割数
vector<int>div0(1,0);
div0[0]=10000;

//a0,a1,..,anの係数用積分区間
double x0=0.0;
double x1=PI;

for(int i=0;i<(int)div0.size();i++)
{
int div=div0[i];
vector<long double>fx;
int ak=11;//展開する Chebyshev関数の次数

//an値の格納部分
vector<long double>Le6_an(ak+1,0.0);

for(int L=ak;L>=0;L--)
{
fx.clear();
int m=L;
for(int i=L*(L+1)/2;i<m+L*(L+1)/2+1;i++) fx.push_back(hx[i]);
fx.resize(fx.size());

double factor=2.0/PI;//Chebyshevの直交係数の逆数

double h=(x1-x0)/div;
double f_xn0=0.0;//分割始点
double f_xn2=0.0;//幅の1/4点
double f_xn3=0.0;//幅の1/3点
double f_xnm=0.0;//中間点
double f_xn6=0.0;//幅の2/3点
double f_xn7=0.0;//幅の3/4点
double f_xn1=0.0;//終点

double g_xn0=0.0;//分割始点
double g_xn2=0.0;//幅の1/4点
double g_xn3=0.0;//幅の1/3点
double g_xnm=0.0;//中間点
double g_xn6=0.0;//幅の2/3点
double g_xn7=0.0;//幅の3/4点
double g_xn1=0.0;//終点

double fg_xn0=0.0;
double fg_xnm=0.0;
double fg_xn1=0.0;

double Le6_ort=0.0;// Gauss-Legendre 6次

for(int j=0;j<div;j++)
{
//Gauss-Legendre
// 6分点
double xLe6_0=x0+j*h+h/2.0+h/2.0*x60;
double xLe6_1=x0+j*h+h/2.0+h/2.0*x61;
double xLe6_2=x0+j*h+h/2.0+h/2.0*x62;
double xLe6_3=x0+j*h+h/2.0+h/2.0*x63;
double xLe6_4=x0+j*h+h/2.0+h/2.0*x64;
double xLe6_5=x0+j*h+h/2.0+h/2.0*x65;

double Le6_0=0.0,Le6_1=0.0,Le6_2=0.0,Le6_3=0.0,Le6_4=0.0,Le6_5=0.0;

for(int i=0;i<m+1;i++)
{
Le6_0=Le6_0+fx[i]*pow(cos(xLe6_0),i);
Le6_1=Le6_1+fx[i]*pow(cos(xLe6_1),i);
Le6_2=Le6_2+fx[i]*pow(cos(xLe6_2),i);
Le6_3=Le6_3+fx[i]*pow(cos(xLe6_3),i);
Le6_4=Le6_4+fx[i]*pow(cos(xLe6_4),i);
Le6_5=Le6_5+fx[i]*pow(cos(xLe6_5),i);
}

double gLe6_0=0.0,gLe6_1=0.0,gLe6_2=0.0,gLe6_3=0.0,gLe6_4=0.0,gLe6_5=0.0;

for(int i=0;i<n;i++)
{
gLe6_0=gLe6_0+gx[i]*pow(cos(xLe6_0),i);
gLe6_1=gLe6_1+gx[i]*pow(cos(xLe6_1),i);
gLe6_2=gLe6_2+gx[i]*pow(cos(xLe6_2),i);
gLe6_3=gLe6_3+gx[i]*pow(cos(xLe6_3),i);
gLe6_4=gLe6_4+gx[i]*pow(cos(xLe6_4),i);
gLe6_5=gLe6_5+gx[i]*pow(cos(xLe6_5),i);
}
Le6_ort=Le6_ort+h/2.0*(wLe6_0*Le6_0*gLe6_0+wLe6_1*Le6_1*gLe6_1+wLe6_2*Le6_2*gLe6_2+
wLe6_3*Le6_3*gLe6_3+wLe6_4*Le6_4*gLe6_4+wLe6_5*Le6_5*gLe6_5);
}//div


Le6_an[L]=Le6_ort*factor;

}//fxの繰り返しに対応

fstream out00an("an_Chebyshev_poly.csv",ios::out |ios::binary |ios::app);
out00an<<"t_"<<"L"<<","<<"div"<<","<<"Le6_an"<<endl;
for(int L=ak;L>=0;L--) out00an<<"t_"<<L<<","<<div<<","<<Le6_an[L]<<endl;
out00an<<" "<<endl;
out00an.close();

vector<double>xn(gx.size(),0.0);
double x=0.0;
int kk=200+1;

vector<double>gx_value(kk,0.0);
for(int j=0;j<kk;j++)
{
x=0.01*j-1.00;
for(int jj=0;jj<(int)gx.size();jj++) xn[jj]=pow(x,(double)jj);
gx_value[j]=inner_product(gx.begin(),gx.end(),xn.begin(),0.0,plus<double>(), multiplies<double>());
}

vector<double>re_Le6(kk,0.0);

for(int j=0;j<kk;j++)
{
x=0.01*j-1.00;
double Le6_sum=0.0;
for(int L=11;L>=3;L--)
{
fx.clear();
int m=L;
for(int i=L*(L+1)/2;i<m+L*(L+1)/2+1;i++) fx.push_back(hx[i]);
fx.resize(fx.size());
for(int i=0;i<m+1;i++)
{
Le6_sum=Le6_sum+Le6_an[L]*fx[i]*pow(x,i);
}
}
re_Le6[j]=Le6_sum;
}

fstream outrecalc11_9_7_5_3("Re-cal_11_9_7_5_3.csv",ios::out |ios::binary |ios::app);
outrecalc11_9_7_5_3<<"div"<<","<<"j"<<","<<"0.01*j-1.00"<<","<<"re_Le6"<<","<<","<<"gx_value"<<endl;
for(int j=0;j<(int)re_Le6.size();j++)
outrecalc11_9_7_5_3<<div<<","<<setw(3)<<j<<","<<0.01*j-1.00<<","<<re_Le6[j]<<","<<gx_value[j]<<endl;
outrecalc11_9_7_5_3<<" "<<endl;
outrecalc11_9_7_5_3.close();


for(int j=0;j<kk;j++)
{

x=0.01*j-1.00;
double Le6_sum=0.0;
for(int L=11;L>=1;L--)
{
fx.clear();
int m=L;
for(int i=L*(L+1)/2;i<m+L*(L+1)/2+1;i++) fx.push_back(hx[i]);
fx.resize(fx.size());
for(int i=0;i<m+1;i++)
{
Le6_sum=Le6_sum+Le6_an[L]*fx[i]*pow(x,i);
}
}
re_Le6[j]=Le6_sum;
}

fstream outrecalc11_9_7_5_3_1("Re-cal_11_9_7_5_3_1.csv",ios::out |ios::binary |ios::app);
outrecalc11_9_7_5_3_1<<"div"<<","<<"j"<<","<<"0.01*j-1.00"<<","<<"re_Le6"<<","<<"gx_value"<<endl;
for(int j=0;j<(int)re_Le6.size();j++)
outrecalc11_9_7_5_3_1<<div<<","<<setw(3)<<j<<","<<0.01*j-1.00<<","<<re_Le6[j]<<","<<gx_value[j]<<endl;
outrecalc11_9_7_5_3_1<<" "<<endl;
outrecalc11_9_7_5_3_1.close();

re_Le6.clear();


}// div0[i]に対応

return 0;
}


vector<double> Chebyshev_function()
{
//Chebyshev関数
vector<double >t0(0+1,0.0);
t0[0]=1.0;

vector<double >t1(1+1,0.0);
t1[0]=0.0;
t1[1]=1.0;

vector<double >t2(2+1,0.0);
t2[0]=-1.0;

// 以下、Chebyshev　多項式参照方


// 以上　Chebyshev多項式　参照方
t35[30]=0.0;
t35[31]=601295421440.0;
t35[32]=0.0;
t35[34]=0.0;
t35[35]=17179869184.0;

int k;
vector<double>hx;
k=0;for(int i=0;i<k+1;i++) hx.push_back(t0[i]);
k=1;for(int i=0;i<k+1;i++) hx.push_back(t1[i]);

// 以下　繰り返しのために削除

// 以上　繰り返しのために削除
k=34;for(int i=0;i<k+1;i++) hx.push_back(t34[i]);
k=35;for(int i=0;i<k+1;i++) hx.push_back(t35[i]);
hx.resize(hx.size());

return hx;
}

本章 7章の説明へ


11、多項式級数展開の係数による Taylor展開の係数算出 ( sin(πx )、 cos( πx ) の場合) コード F-1

#include <cmath>
#include <fstream>
#include <vector>
#include <iomanip>
#include <numeric>
#include <iostream>
#include <array>
using namespace std;

const long double PI=3.14159265358979323846264338327950288;

vector<double> Legendre_function();
vector<double> Chebyshev_function();
long long recursive_call_for_factorial(int n );//n!

double g_function(double x,double a, double b)
{ return sin(PI*x*a+b);}

//直交関数の多項式による多項式展開とTayler展開
int main()
{

vector<double>hx_Le;
hx_Le=Legendre_function();
hx_Le.resize(hx_Le.size());

vector<double>hx_Ch;
hx_Ch=Chebyshev_function();
hx_Ch.resize(hx_Ch.size());

double a=1.0;
double b=PI/2.0;

//Gauss-Legendre
// 6分点　分点
double x60=-0.93246951420315;
double x61=-0.661209386466265;
double x62=-0.238619186083197;
double x63=0.238619186083197;
double x64=0.661209386466265;
double x65=0.93246951420315;
//重み係数
double wLe6_0=0.171324492379176;
double wLe6_1=0.360761573048438;
double wLe6_2=0.467913934572691;
double wLe6_3=0.467913934572691;
double wLe6_4=0.360761573048438;
double wLe6_5=0.171324492379176;

vector<int>div0(0+1,0);//
div0[0]=10000;


//a0,a1,..,anの係数用積分区間
double x0_Le=-1.0;
double x1_Le=1.0;

//a0,a1,..,anの係数用積分区間
double x0_Ch=0.0;
double x1_Ch=PI;

for(int i=0;i<(int)div0.size();i++)
{
int div=div0[i];

vector<long double>fx_Le;
vector<long double>fx_Ch;

int k_Ch,k_Le;//展開するLegendre関数の次数
k_Le=k_Ch=16;


//an値の格納部分
vector<long double>an_Le(k_Le+1,0.0);
vector<long double>an_Ch(k_Ch+1,0.0);

for(int L=k_Le;L>=0;L--)
{
fx_Le.clear();
fx_Ch.clear();

int m=L;

for(int i=L*(L+1)/2;i<m+L*(L+1)/2+1;i++) fx_Le.push_back(hx_Le[i]);
fx_Le.resize(fx_Le.size());

for(int i=L*(L+1)/2;i<m+L*(L+1)/2+1;i++) fx_Ch.push_back(hx_Ch[i]);
fx_Ch.resize(fx_Ch.size());

double factor_Le=(2.0*L+1)/2.0;//Legendreの直交係数の逆数
double factor_Ch=2.0/PI;//Legendreの直交係数の逆数　正規化
double factor_ChL0=1.0/PI;//Legendreの直交係数の逆数　正規化


double h_Le=(x1_Le-x0_Le)/div;
double h_Ch=(x1_Ch-x0_Ch)/div;

double f_xn0=0.0;//分割始点
double f_xn2=0.0;//幅の1/4点
double f_xn3=0.0;//幅の1/3点
double f_xnm=0.0;//中間点
double f_xn6=0.0;//幅の2/3点
double f_xn7=0.0;//幅の3/4点
double f_xn1=0.0;//終点

double g_xn0=0.0;//分割始点
double g_xn2=0.0;//幅の1/4点
double g_xn3=0.0;//幅の1/3点
double g_xnm=0.0;//中間点
double g_xn6=0.0;//幅の2/3点
double g_xn7=0.0;//幅の3/4点
double g_xn1=0.0;//終点

double ort_Le=0.0;// Gauss-Legendre 6次
double ort_Ch=0.0;// Gauss-Legendre 6分点


for(int j=0;j<div;j++)
{

//Gauss-Legendre
// 6分点
double xLe6_0=x0_Le+j*h_Le+h_Le/2.0+h_Le/2.0*x60;
double xLe6_1=x0_Le+j*h_Le+h_Le/2.0+h_Le/2.0*x61;
double xLe6_2=x0_Le+j*h_Le+h_Le/2.0+h_Le/2.0*x62;
double xLe6_3=x0_Le+j*h_Le+h_Le/2.0+h_Le/2.0*x63;
double xLe6_4=x0_Le+j*h_Le+h_Le/2.0+h_Le/2.0*x64;
double xLe6_5=x0_Le+j*h_Le+h_Le/2.0+h_Le/2.0*x65;

double Le6_0=0.0,Le6_1=0.0,Le6_2=0.0,Le6_3=0.0,Le6_4=0.0,Le6_5=0.0;

for(int i=0;i<m+1;i++)
{
Le6_0=Le6_0+fx_Le[i]*(double)pow(xLe6_0,i);
Le6_1=Le6_1+fx_Le[i]*(double)pow(xLe6_1,i);
Le6_2=Le6_2+fx_Le[i]*(double)pow(xLe6_2,i);
Le6_3=Le6_3+fx_Le[i]*(double)pow(xLe6_3,i);
Le6_4=Le6_4+fx_Le[i]*(double)pow(xLe6_4,i);
Le6_5=Le6_5+fx_Le[i]*(double)pow(xLe6_5,i);
}

double gLe6_0=0.0,gLe6_1=0.0,gLe6_2=0.0,gLe6_3=0.0,gLe6_4=0.0,gLe6_5=0.0;

gLe6_0=g_function(xLe6_0,a,b);
gLe6_1=g_function(xLe6_1,a,b);
gLe6_2=g_function(xLe6_2,a,b);
gLe6_3=g_function(xLe6_3,a,b);
gLe6_4=g_function(xLe6_4,a,b);
gLe6_5=g_function(xLe6_5,a,b);

ort_Le=ort_Le+h_Le/2.0*(wLe6_0*Le6_0*gLe6_0+wLe6_1*Le6_1*gLe6_1+wLe6_2*Le6_2*gLe6_2
+wLe6_3*Le6_3*gLe6_3+wLe6_4*Le6_4*gLe6_4+wLe6_5*Le6_5*gLe6_5);


// chbyshev poly
//Gauss-Legendre
// 6分点
xLe6_0=x0_Ch+j*h_Ch+h_Ch/2.0+h_Ch/2.0*x60;
xLe6_1=x0_Ch+j*h_Ch+h_Ch/2.0+h_Ch/2.0*x61;
xLe6_2=x0_Ch+j*h_Ch+h_Ch/2.0+h_Ch/2.0*x62;
xLe6_3=x0_Ch+j*h_Ch+h_Ch/2.0+h_Ch/2.0*x63;
xLe6_4=x0_Ch+j*h_Ch+h_Ch/2.0+h_Ch/2.0*x64;
xLe6_5=x0_Ch+j*h_Ch+h_Ch/2.0+h_Ch/2.0*x65;

Le6_0=0.0,Le6_1=0.0,Le6_2=0.0,Le6_3=0.0,Le6_4=0.0,Le6_5=0.0;

for(int i=0;i<m+1;i++)
{
Le6_0=Le6_0+fx_Ch[i]*(double)pow((double)cos(xLe6_0),i);
Le6_1=Le6_1+fx_Ch[i]*(double)pow((double)cos(xLe6_1),i);
Le6_2=Le6_2+fx_Ch[i]*(double)pow((double)cos(xLe6_2),i);
Le6_3=Le6_3+fx_Ch[i]*(double)pow((double)cos(xLe6_3),i);
Le6_4=Le6_4+fx_Ch[i]*(double)pow((double)cos(xLe6_4),i);
Le6_5=Le6_5+fx_Ch[i]*(double)pow((double)cos(xLe6_5),i);
}

gLe6_0=0.0,gLe6_1=0.0,gLe6_2=0.0,gLe6_3=0.0,gLe6_4=0.0,gLe6_5=0.0;

gLe6_0=g_function((double)cos(xLe6_0),a,b);
gLe6_1=g_function((double)cos(xLe6_1),a,b);
gLe6_2=g_function((double)cos(xLe6_2),a,b);
gLe6_3=g_function((double)cos(xLe6_3),a,b);
gLe6_4=g_function((double)cos(xLe6_4),a,b);
gLe6_5=g_function((double)cos(xLe6_5),a,b);

ort_Ch=ort_Ch+h_Ch/2.0*(wLe6_0*Le6_0*gLe6_0+wLe6_1*Le6_1*gLe6_1+wLe6_2*Le6_2*gLe6_2
+wLe6_3*Le6_3*gLe6_3+wLe6_4*Le6_4*gLe6_4+wLe6_5*Le6_5*gLe6_5);

}//div

cout<<"p&t_"<<L<<","<<div<<endl;

an_Le[L]=ort_Le*factor_Le;
an_Ch[L]=ort_Ch*factor_Ch;
if(L==0){ an_Ch[L]=ort_Ch*factor_ChL0;}


}//fx_Leの繰り返しに対応


fstream out00an("Value_of_an_Le_Ch.csv",ios::out |ios::binary |ios::app);
out00an<<"p&t_"<<"L"<<","<<"div"<<","<<"an_Le"<<","<<"an_Ch"<<","<<endl;
for(int L=k_Le;L>=0;L--) out00an<<"p$t_"<<L<<","<<div<<","<<setprecision(20)<<an_Le[L]<<","<<an_Ch[L]<<","<<endl;
out00an<<" "<<endl;
out00an.close();


long double x=0.0;
int kk=200+1;

vector<long double>gx_value(kk,0.0);
for(int j=0;j<kk;j++)
{
x=0.01*j-1.0;
gx_value[j]=g_function(x,a,b);
}

vector<long double>re_Le(kk,0.0),re_Ch(kk,0.0);
double c0_Le[50][50],c0_Ch[50][50];

for(int i=0;i<50;i++)//別データ混入防止のための初期化
{
for(int j=0;j<50;j++)
{
c0_Le[i][j]=0.0;
c0_Ch[i][j]=0.0;
}
}


for(int j=0;j<kk;j++)
{
x=0.01*j-1.0;
double sum_Le=0.0;
double sum_Ch=0.0;

for(int L=k_Le;L>=0;L=L-2)
{
fx_Le.clear();
fx_Ch.clear();

int m=L;

for(int i=L*(L+1)/2;i<m+L*(L+1)/2+1;i++)
{
fx_Le.push_back(hx_Le[i]);
fx_Ch.push_back(hx_Ch[i]);
}
fx_Le.resize(fx_Le.size());
fx_Ch.resize(fx_Ch.size());

for(int i=0;i<m+1;i++)
{
sum_Le=sum_Le+(double)an_Le[L]*(double)fx_Le[i]*(double)pow(x,i);
sum_Ch=sum_Ch+(double)an_Ch[L]*(double)fx_Ch[i]*(double)pow(x,i);
c0_Le[L][i]=(double)fx_Le[i];
c0_Ch[L][i]=(double)fx_Ch[i];
}
}
re_Le[j]=sum_Le;
re_Ch[j]=sum_Ch;

}

re_Le.clear();
re_Ch.clear();

vector<long double>tayler_Le(k_Le+1,0.0);
vector<long double>tayler_Ch(k_Ch+1,0.0);

//for(int L=1;L<k_Le+1;L=L+2)//sin
for(int L=0;L<k_Le+1;L=L+2)//cos
{
int m=L;
for(int i=m;i<k_Le+1;i=i+2)
{
tayler_Le[L]=tayler_Le[L]+an_Le[i]*c0_Le[i][L];
tayler_Ch[L]=tayler_Ch[L]+an_Ch[i]*c0_Ch[i][L];
}
}


fstream out03("Tayler_0.csv",ios::out |ios::binary |ios::app);
out03<<"分割数"<<","<<"次数"<<","<<"tayler_Le算出値"<<","<<"tayler_Ch算出値"
<<","<<","<<"tayler_真値"<<","<<","<<"(Le-真値)/真値"<<","<<"%"<<","<<"(Ch-真値)/真値"<<","<<"%"<<endl;

for(int L=k_Le;L>=0;L=L-2)
{
// long long fa=recursive_call_for_factorial(L);
double ta=(double)pow(PI,L)/recursive_call_for_factorial(L);

// if((L-1)/4.0 !=int((L-1)/4.0)) ta=-ta;// sin
if((L)/4.0 !=int((L)/4.0)) ta=-ta;//cos

out03<<div<<","<<L<<","<<setprecision(30)<<tayler_Le[L]<<","<<setprecision(30)<<tayler_Ch[L]<<","
<<","<<ta<<","<<","<<(tayler_Le[L]-ta)/ta*100<<","<<"%"<<","<<(tayler_Ch[L]-ta)/ta*100<<","<<"%"<<endl;


}
out03<<" "<<endl;
out03.close();

}// div0[i]に対応

return 0;
}


vector<double> Legendre_function()
{
//Legendre関数p　
vector<double >p0(0+1,0.0);
p0[0]=1.0;

vector<double >p1(1+1,0.0);
p1[0]=0.0;
p1[1]=1.0;

vector<double >p2(2+1,0.0);
p2[0]=-1/2.0;
p2[1]=0.0;
p2[2]=3/2.0;

//以下　既に別記故削除


//以上、既に別記故に削除
p34[31]=0.0;
p34[32]=-13867459395.116700;// .1167以降0が続く
//p34[32]=-59560284580634192355/4294967296.0;//error C2177:定数が大
p34[33]=0.0;
p34[34]=7113260368810144185/4294967296.0;


int k;
vector<double>hx;
k=0;for(int i=0;i<k+1;i++) hx.push_back(p0[i]);
k=1;for(int i=0;i<k+1;i++) hx.push_back(p1[i]);

//　以下　既に繰り返し故削除


//　以上、繰り返し故に削除
k=34;for(int i=0;i<k+1;i++) hx.push_back(p34[i]);
hx.resize(hx.size());

return hx;

}


vector<double> Chebyshev_function()
{
//Chebyshev関数
vector<double >t0(0+1,0.0);
t0[0]=1.0;

vector<double >t1(1+1,0.0);
t1[0]=0.0;
t1[1]=1.0;

vector<double >t2(2+1,0.0);
t2[0]=-1.0;
t2[1]=0.0;
t2[2]=2.0;

//以下 別記故に削除



//以上　別記故に削除
t35[34]=0.0;
t35[35]=17179869184.0;

int k;
vector<double>hx;
k=0;for(int i=0;i<k+1;i++) hx.push_back(t0[i]);
k=1;for(int i=0;i<k+1;i++) hx.push_back(t1[i]);
k=2;for(int i=0;i<k+1;i++) hx.push_back(t2[i]);

//以下　繰り返し故に削除


// 以上　繰り返し故に削除
k=35;for(int i=0;i<k+1;i++) hx.push_back(t35[i]);
hx.resize(hx.size());

return hx;

}

long long recursive_call_for_factorial(int n )//n!
{
if(n == 0 || n==1) return 1;//0! or 1! = 1
else
return n*recursive_call_for_factorial(n-1);
}









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