232 Chapter 6.Special Functions a=Vr()m(x)+o.()x 6.5.10) where 2m+1 Xn三x- (6.5.11) and where Po,P,Qo,and Q1 are each polynomials in their arguments,for 0< 8/z<1.The P's are even polynomials,the Q's odd. Coefficients of the various rational functions and polynomials are given by Hart [1],for various levels of desired accuracy.A straightforward implementation is 鱼 nted for 19881992 #include <math.h> 1-800 float bessj0(float x) Returns the Bessel function Jo(x)for any real x. float ax,z; double xx,y,ans,ans1,ans2; Accumulate polynomials in double precision. (Nor if ((ax=fabs(x))<8.0){ Direct rational function fit. y=x*x: America server computer, one paper University Press. THE ans1=57568490574.0+y*(-13362590354.0+y*(651619640.7 +y*(-11214424.18+y*(77392.33017+y*(-184.9052456)): ART ans2=57568490411.0+y*(1029532985.0+y*(9494680.718 是 +y*(59272.64853+y*(267.8532712+y*1.0)))); ans eans1/ans2; Programs else Fitting function (6.5.9) z=8.0/ax; st st y=2*z; xx=ax-0.785398164; Copyright (C) ans1=1.0+y*(-0.1098628627e-2+y*(0.2734510407e-4 +y*(-0.2073370639e-5+y*0.20938872118-6)); ans2=-0.1562499995e-1+y*(0.1430488765e-3 +y*(-0.6911147651e-5+y*(0.7621095161e-6 email to directcustsen -y*0.934945152e-7))）; ans=sqrt(0.636619772/ax)*(cos(xx)*ans1-z*sin(xx)*ans2); OF SCIENTIFIC COMPUTING(ISBN 0-521- return ans; @cambridge.org 1988-1992 by Numerical Recipes -431085 #include <math.h> float bessy0(float x) Software. Returns the Bessel function Yo(x)for positive x. float bessjo(float x); (outside North America) 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*x: ans1=-2957821389.0+y*(7062834065.0+y*(-512359803.6 +y*(10879881.29+y*(-86327.92757+y*228.4622733))); ans2=40076544269.0+y*(745249964.8+y*(7189466.438 +y*(47447.26470+y*(226.1030244+y*1.0)))); ans=(ans1/ans2)+0.636619772*bessj0(x)*1og(x); else Fitting function (6.5.10)232 Chapter 6. Special Functions 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). Yn(x) =  2 πx  Pn
8 x sin(Xn) + Qn
8 x cos(Xn)  (6.5.10) where Xn ≡ x − 2n + 1 4 π (6.5.11) and where P0, P1, Q0, and Q1 are each polynomials in their arguments, for 0 < 8/x < 1. The P’s are even polynomials, the Q’s odd. Coefficients of the various rational functions and polynomials are given by Hart [1], for various levels of desired accuracy. A straightforward implementation is #include <math.h> float bessj0(float x) Returns the Bessel function J0(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 function fit. y=x*x; ans1=57568490574.0+y*(-13362590354.0+y*(651619640.7 +y*(-11214424.18+y*(77392.33017+y*(-184.9052456))))); ans2=57568490411.0+y*(1029532985.0+y*(9494680.718 +y*(59272.64853+y*(267.8532712+y*1.0)))); ans=ans1/ans2; } else { Fitting function (6.5.9). z=8.0/ax; y=z*z; xx=ax-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/ax)*(cos(xx)*ans1-z*sin(xx)*ans2); } return ans; } #include <math.h> float bessy0(float x) Returns the Bessel function Y0(x) for positive x. { float bessj0(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 = -2957821389.0+y*(7062834065.0+y*(-512359803.6 +y*(10879881.29+y*(-86327.92757+y*228.4622733)))); ans2=40076544269.0+y*(745249964.8+y*(7189466.438 +y*(47447.26470+y*(226.1030244+y*1.0)))); ans=(ans1/ans2)+0.636619772*bessj0(x)*log(x); } else { Fitting function (6.5.10).