6.5 Bessel Functions of Integer Order 233 z=8.0/x; y=2*2; xx=x-0.785398164; ans1=1.0+y*(-0.1098628627e-2+y*(0.2734510407e-4 +y*(-0.2073370639e-5+y*0.2093887211a-6)); ans2=-0.1562499995e-1+y*(0.1430488765e-3 +y*(-0.6911147651e-5+y*(0.7621095161e-6 +y*(-0.934945152e-7)))): ans=sqrt(0.636619772/x)*(sin(xx)*ans1+z*cos(xx)*ans2); return ans; 2 http://www.n Permission is read able files #include <math.h> .com or call (including this one) granted fori 19881992 float bessj1(float x) 11-800 Returns the Bessel function J(x)for any real x. float ax,z; to any double xx,y,ans,ans1,ans2; Accumulate polynomials in double precision. from NUMERICAL RECIPES IN if ((ax=fabs(x))<8.0){ Direct rational approximation y=x*x: ans1=x*(72362614232.0+y*(-7895059235.0+y*(242396853.1 +y*(-2972611.439+y*(15704.48260+y*(-30.16036606))))); (North America server computer, Cambridge University Press. tusers to make THE ans2=144725228442.0+y*(2300535178.0+y*(18583304.74 one paper ART +y*(99447.43394+y*(376.9991397+y*1.0)))); 是 ans=ans1/ans2; else Fitting function (6.5.9) Programs z=8.0/ax: send y=2*2; xx=ax-2.356194491: ans1=1.0+y*(0.183105e-2+y*(-0.3516396496e-4 +y*(0.2457520174e-5+y*(-0.240337019e-6)))); ans2=0.04687499995+y*(-0.2002690873e-3 +y*(0.8449199096e-5+y*(-0.88228987e-6 +y*0.105787412e-6))); email to directcustsen ans=sqrt (0.636619772/ax)*(cos(xx)*ans1-z*sin(xx)*ans2); if (x 0.0)ans -ans; OF SCIENTIFIC COMPUTING(ISBN 0-521- 2 return ans; @cambridge.org 1988-1992 by Numerical Recipes -43106 #include <math.h> float bessy1(float x) Returns the Bessel function Y1(x)for positive x. float bessj1(float x); (outside North America) Software. float zi double xx,y,ans,ans1,ans2; Accumulate polynomials in double precision. if(x<8.0) Rational function approximation of(6.5.8) y=*x: ans1=x*(-0.4900604943e13+y*(0.1275274390e13 +y*(-0.5153438139e11+y*(0.7349264551e9 +y*(-0.4237922726e7+y*0.8511937935e4))); ans2=0.2499580570e14+y*(0.4244419664e12 +y*(0.3733650367e10+y*(0.2245904002e8 +y*(0.1020426050e6+y*(0.3549632885e3+y)))):6.5 Bessel Functions of Integer Order 233 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). z=8.0/x; y=z*z; xx=x-0.785398164; ans1=1.0+y*(-0.1098628627e-2+y*(0.2734510407e-4 +y*(-0.2073370639e-5+y*0.2093887211e-6))); ans2 = -0.1562499995e-1+y*(0.1430488765e-3 +y*(-0.6911147651e-5+y*(0.7621095161e-6 +y*(-0.934945152e-7)))); ans=sqrt(0.636619772/x)*(sin(xx)*ans1+z*cos(xx)*ans2); } return ans; } #include <math.h> float bessj1(float x) Returns the Bessel function J1(x) for any real x. { float ax,z; double xx,y,ans,ans1,ans2; Accumulate polynomials in double precision. if ((ax=fabs(x)) < 8.0) { Direct rational approximation. y=x*x; ans1=x*(72362614232.0+y*(-7895059235.0+y*(242396853.1 +y*(-2972611.439+y*(15704.48260+y*(-30.16036606)))))); ans2=144725228442.0+y*(2300535178.0+y*(18583304.74 +y*(99447.43394+y*(376.9991397+y*1.0)))); ans=ans1/ans2; } else { Fitting function (6.5.9). z=8.0/ax; y=z*z; xx=ax-2.356194491; ans1=1.0+y*(0.183105e-2+y*(-0.3516396496e-4 +y*(0.2457520174e-5+y*(-0.240337019e-6)))); ans2=0.04687499995+y*(-0.2002690873e-3 +y*(0.8449199096e-5+y*(-0.88228987e-6 +y*0.105787412e-6))); ans=sqrt(0.636619772/ax)*(cos(xx)*ans1-z*sin(xx)*ans2); if (x < 0.0) ans = -ans; } return ans; } #include <math.h> float bessy1(float x) Returns the Bessel function Y1(x) for positive x. { float bessj1(float x); float z; double xx,y,ans,ans1,ans2; Accumulate polynomials in double precision. if (x < 8.0) { Rational function approximation of (6.5.8). y=x*x; ans1=x*(-0.4900604943e13+y*(0.1275274390e13 +y*(-0.5153438139e11+y*(0.7349264551e9 +y*(-0.4237922726e7+y*0.8511937935e4))))); ans2=0.2499580570e14+y*(0.4244419664e12 +y*(0.3733650367e10+y*(0.2245904002e8 +y*(0.1020426050e6+y*(0.3549632885e3+y)))));