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#include <math.h>
/*
floating point Bessel's function of
the first and second kinds and of
integer order.
int n;
double x;
jn(n,x);
returns the value of Jn(x) for all
integer values of n and all real values
of x.
There are no error returns.
Calls j0, j1.
For n=0, j0(x) is called,
for n=1, j1(x) is called,
for n<x, forward recursion us used starting
from values of j0(x) and j1(x).
for n>x, a continued fraction approximation to
j(n,x)/j(n-1,x) is evaluated and then backward
recursion is used starting from a supposed value
for j(n,x). The resulting value of j(0,x) is
compared with the actual value to correct the
supposed value of j(n,x).
yn(n,x) is similar in all respects, except
that forward recursion is used for all
values of n>1.
*/
double jn(int n, double x)
{
int i, sign;
double a, b, temp;
double xsq, t;
/*
n
J (x) = (-1) J (x)
-n n
n
J (-x) = (-1) J (x)
n n
*/
sign = 1;
if(n<0){
n = -n;
if( n & 1 )
sign = -1;
}
if( x < 0.0 )
{
if( n & 1 )
sign = -sign;
x = -x;
}
if(n==0) return(j0(x));
if(n==1) return(sign*j1(x));
if(x == 0.) return(0.);
if(n>x) goto recurs;
/* Note, forward recurrence for Jn is numerically unstable.
This should be fixed sometime. */
a = j0(x);
b = j1(x);
for(i=1;i<n;i++){
temp = b;
b = (2.*i/x)*b - a;
a = temp;
}
return(sign*b);
recurs:
xsq = x*x;
for(t=0,i=n+16;i>n;i--){
t = xsq/(2.*i - t);
}
t = x/(2.*n-t);
a = t;
b = 1;
for(i=n-1;i>0;i--){
temp = b;
b = (2.*i/x)*b - a;
a = temp;
}
return(sign*t*j0(x)/b);
}
double yn(int n, double x)
{
int i;
int sign;
double a, b, temp;
if (x <= 0) {
return(-HUGE_VAL);
}
sign = 1;
if(n<0){
n = -n;
if(n%2 == 1) sign = -1;
}
if(n==0) return(y0(x));
if(n==1) return(sign*y1(x));
a = y0(x);
b = y1(x);
for(i=1;i<n;i++){
temp = b;
b = (2.*i/x)*b - a;
a = temp;
}
return(sign*b);
}
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