File:  [Research Unix] / researchv10dc / asm.libm / jn.c
Revision 1.1.1.1 (vendor branch): download - view: text, annotated - select for diffs
Tue Apr 24 17:21:34 2018 UTC (3 years, 9 months ago) by root
Branches: belllabs, MAIN
CVS tags: researchv10, HEAD
```researchv10 Dan Cross
```

```/*
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.
*/

#include <math.h>
#include <errno.h>

int	errno;

double
jn(n,x) int n; double x;{
int i;
double a, b, temp;
double xsq, t;
double j0(), j1();

if(n<0){
n = -n;
x = -x;
}
if(n==0) return(j0(x));
if(n==1) return(j1(x));
if(x == 0.) return(0.);
if(n>x) goto recurs;

a = j0(x);
b = j1(x);
for(i=1;i<n;i++){
temp = b;
b = (2.*i/x)*b - a;
a = temp;
}
return(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(t*j0(x)/b);
}

double
yn(n,x) int n; double x;{
int i;
int sign;
double a, b, temp;
double y0(), y1();

if (x <= 0) {
errno = EDOM;
return(-HUGE);
}
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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