/*	floating point Bessel's function	of the first and second kinds	of order zero	j0(x) returns the value of J0(x)	for all real values of x.	There are no error returns.	Calls sin, cos, sqrt.	There is a niggling bug in J0 which	causes errors up to 2e-16 for x in the	interval [-8,8].	The bug is caused by an inappropriate order	of summation of the series.  rhm will fix it	someday.	Coefficients are from Hart & Cheney.	#5849 (19.22D)	#6549 (19.25D)	#6949 (19.41D)	y0(x) returns the value of Y0(x)	for positive real values of x.	For x<=0, error number EDOM is set and a	large negative value is returned.	Calls sin, cos, sqrt, log, j0.	The values of Y0 have not been checked	to more than ten places.	Coefficients are from Hart & Cheney.	#6245 (18.78D)	#6549 (19.25D)	#6949 (19.41D)*/#include <math.h>#include <errno.h>int	errno;static double pzero, qzero;static double tpi	= .6366197723675813430755350535e0;static double pio4	= .7853981633974483096156608458e0;static double p1[] = {	0.4933787251794133561816813446e21,	-.1179157629107610536038440800e21,	0.6382059341072356562289432465e19,	-.1367620353088171386865416609e18,	0.1434354939140344111664316553e16,	-.8085222034853793871199468171e13,	0.2507158285536881945555156435e11,	-.4050412371833132706360663322e8,	0.2685786856980014981415848441e5,};static double q1[] = {	0.4933787251794133562113278438e21,	0.5428918384092285160200195092e19,	0.3024635616709462698627330784e17,	0.1127756739679798507056031594e15,	0.3123043114941213172572469442e12,	0.6699987672982239671814028660e9,	0.1114636098462985378182402543e7,	0.1363063652328970604442810507e4,	1.0};static double p2[] = {	0.5393485083869438325262122897e7,	0.1233238476817638145232406055e8,	0.8413041456550439208464315611e7,	0.2016135283049983642487182349e7,	0.1539826532623911470917825993e6,	0.2485271928957404011288128951e4,	0.0,};static double q2[] = {	0.5393485083869438325560444960e7,	0.1233831022786324960844856182e8,	0.8426449050629797331554404810e7,	0.2025066801570134013891035236e7,	0.1560017276940030940592769933e6,	0.2615700736920839685159081813e4,	1.0,};static double p3[] = {	-.3984617357595222463506790588e4,	-.1038141698748464093880530341e5,	-.8239066313485606568803548860e4,	-.2365956170779108192723612816e4,	-.2262630641933704113967255053e3,	-.4887199395841261531199129300e1,	0.0,};static double q3[] = {	0.2550155108860942382983170882e6,	0.6667454239319826986004038103e6,	0.5332913634216897168722255057e6,	0.1560213206679291652539287109e6,	0.1570489191515395519392882766e5,	0.4087714673983499223402830260e3,	1.0,};static double p4[] = {	-.2750286678629109583701933175e20,	0.6587473275719554925999402049e20,	-.5247065581112764941297350814e19,	0.1375624316399344078571335453e18,	-.1648605817185729473122082537e16,	0.1025520859686394284509167421e14,	-.3436371222979040378171030138e11,	0.5915213465686889654273830069e8,	-.4137035497933148554125235152e5,};static double q4[] = {	0.3726458838986165881989980e21,	0.4192417043410839973904769661e19,	0.2392883043499781857439356652e17,	0.9162038034075185262489147968e14,	0.2613065755041081249568482092e12,	0.5795122640700729537480087915e9,	0.1001702641288906265666651753e7,	0.1282452772478993804176329391e4,	1.0,};doublej0(arg) double arg;{	double argsq, n, d;	double sin(), cos(), sqrt();	int i;	if(arg < 0.) arg = -arg;	if(arg > 8.){		asympt(arg);		n = arg - pio4;		return(sqrt(tpi/arg)*(pzero*cos(n) - qzero*sin(n)));	}	argsq = arg*arg;	for(n=0,d=0,i=8;i>=0;i--){		n = n*argsq + p1[i];		d = d*argsq + q1[i];	}	return(n/d);}doubley0(arg) double arg;{	double argsq, n, d;	double sin(), cos(), sqrt(), log(), j0();	int i;	errno = 0;	if(arg <= 0.){		errno = EDOM;		return(-HUGE);	}	if(arg > 8.){		asympt(arg);		n = arg - pio4;		return(sqrt(tpi/arg)*(pzero*sin(n) + qzero*cos(n)));	}	argsq = arg*arg;	for(n=0,d=0,i=8;i>=0;i--){		n = n*argsq + p4[i];		d = d*argsq + q4[i];	}	return(n/d + tpi*j0(arg)*log(arg));}staticasympt(arg) double arg;{	double zsq, n, d;	int i;	zsq = 64./(arg*arg);	for(n=0,d=0,i=6;i>=0;i--){		n = n*zsq + p2[i];		d = d*zsq + q2[i];	}	pzero = n/d;	for(n=0,d=0,i=6;i>=0;i--){		n = n*zsq + p3[i];		d = d*zsq + q3[i];	}	qzero = (8./arg)*(n/d);}