6.7 Bessel Functions of Fractional Order 245 cr=br+cr*fact; ci=bi-ci*fact: if (fabs(cr)+fabs(ci)<FPMIN)cr-FPMIN; den=dr*dr+di*di; dr /den; di /=-den; dlr=cr*dr-ci*di; dli=cr*di+ci*dr; temp=p*dlr-q*dli; q-p*dli+q*dlr; p=temp; if (fabs(dlr-1.0)+fabs(dli)<EPS)break: http://www.nr. readable files Permission is if (i>MAXIT)nrerror("cf2 failed in bessjy"); gam=(p-f)/q; Equations(6.7.6)-(6.7.10) rjmu=sqrt(w/((p-f)*gam+q)); .com or call granted fori rjmu=SIGN(rjmu,rjl); rymu=rjmu*gam; rymup=rymu*(p+q/gam); ry1=xmu*xi*rymu-rymup; 11-800-872 (including this one) fact=rjmu/rjl; *ri=ril1*fact; Scale original J and J *rjp=rjpi*fact; for (i=1;i<=nl;i++) Upward recurrence of yo rytemp=(xmu+i)*xi2*ry1-rymu 7423 (North America to any server computer,is strictly prohibited. tusers to make one paper 1988-1992 by Cambridge University Press.Programs from NUMERICAL RECIPES IN C: THE rymu=ry1; ry1=rytemp; only), *ry=rymu; *ryp=xnu*xi*rymu-ry1; copy for their #define NUSE1 5 mail to directcustsen Copyright(C) #define NUSE2 5 ART OF SCIENTIFIC COMPUTING(ISBN 0-521 void beschb(double x,double *gam1,double *gam2,double *gampl,double *gammi) Evaluates I1 and T2 by Chebyshev expansion for x<1/2.Also returns 1/T(1+x)and v@cambr 1/T(1-x).If converting to double precision,set NUSE1 7,NUSE2 =8. float chebev(float a,float b,float c[],int m,float x); To order Numerical Recipes books or 1988-1992 by Numerical Recipes float xx; -431085 static f1oatc1[▣={ -1.142022680371168e0,6.5165112670737e-3, 3.087090173086e-4,-3.4706269649e-6,6.9437664e-9 3.67795e-11,-1.356e-13}: Software. static float c2[]= 1.843740587300905e0,-7.68528408447867e-2, (outside North America) 1.2719271366546e-3,-4.9717367042e-6,-3.31261198e-8, 2.423096e-10,-1.702e-13,-1.49e-15]; ying of machine Xx=8.0*x*x-1.0; Multiply x by 2 to make range be-1 to 1, *gam1=chebev(-1.0,1.0,c1,NUSE1,xx); and then apply transformation for eval- *gam2=chebev(-1.0,1.0,c2,NUSE2,xx) uating even Chebyshev series. *gampl=*gam2-x*(*gam1) *gammi=*gam2+x*(*gam1);6.7 Bessel Functions of Fractional Order 245 Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyin Copyright (C) 1988-1992 by Cambridge University Press. Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) g of machine￾readable files (including this one) to any server computer, is strictly prohibited. To order Numerical Recipes books or CDROMs, visit website http://www.nr.com or call 1-800-872-7423 (North America only), or send email to directcustserv@cambridge.org (outside North America). cr=br+cr*fact; ci=bi-ci*fact; if (fabs(cr)+fabs(ci) < FPMIN) cr=FPMIN; den=dr*dr+di*di; dr /= den; di /= -den; dlr=cr*dr-ci*di; dli=cr*di+ci*dr; temp=p*dlr-q*dli; q=p*dli+q*dlr; p=temp; if (fabs(dlr-1.0)+fabs(dli) < EPS) break; } if (i > MAXIT) nrerror("cf2 failed in bessjy"); gam=(p-f)/q; Equations (6.7.6) – (6.7.10). rjmu=sqrt(w/((p-f)*gam+q)); rjmu=SIGN(rjmu,rjl); rymu=rjmu*gam; rymup=rymu*(p+q/gam); ry1=xmu*xi*rymu-rymup; } fact=rjmu/rjl; *rj=rjl1*fact; Scale original Jν and J
ν. *rjp=rjp1*fact; for (i=1;i<=nl;i++) { Upward recurrence of Yν. rytemp=(xmu+i)*xi2*ry1-rymu; rymu=ry1; ry1=rytemp; } *ry=rymu; *ryp=xnu*xi*rymu-ry1; } #define NUSE1 5 #define NUSE2 5 void beschb(double x, double *gam1, double *gam2, double *gampl, double *gammi) Evaluates Γ1 and Γ2 by Chebyshev expansion for |x| ≤ 1/2. Also returns 1/Γ(1 + x) and 1/Γ(1 − x). If converting to double precision, set NUSE1 = 7, NUSE2 = 8. { float chebev(float a, float b, float c[], int m, float x); float xx; static float c1[] = { -1.142022680371168e0,6.5165112670737e-3, 3.087090173086e-4,-3.4706269649e-6,6.9437664e-9, 3.67795e-11,-1.356e-13}; static float c2[] = { 1.843740587300905e0,-7.68528408447867e-2, 1.2719271366546e-3,-4.9717367042e-6,-3.31261198e-8, 2.423096e-10,-1.702e-13,-1.49e-15}; xx=8.0*x*x-1.0; Multiply x by 2 to make range be −1 to 1, and then apply transformation for eval￾uating even Chebyshev series. *gam1=chebev(-1.0,1.0,c1,NUSE1,xx); *gam2=chebev(-1.0,1.0,c2,NUSE2,xx); *gampl= *gam2-x*(*gam1); *gammi= *gam2+x*(*gam1); }