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/* jnl.c
*
* Bessel function of integer order
*
*
*
* SYNOPSIS:
*
* int n;
* long double x, y, jnl();
*
* y = jnl( n, x );
*
*
*
* DESCRIPTION:
*
* Returns Bessel function of order n, where n is a
* (possibly negative) integer.
*
* The ratio of jn(x) to j0(x) is computed by backward
* recurrence. First the ratio jn/jn-1 is found by a
* continued fraction expansion. Then the recurrence
* relating successive orders is applied until j0 or j1 is
* reached.
*
* If n = 0 or 1 the routine for j0 or j1 is called
* directly.
*
*
*
* ACCURACY:
*
* Absolute error:
* arithmetic domain # trials peak rms
* IEEE -30, 30 5000 3.3e-19 4.7e-20
*
*
* Not suitable for large n or x.
*
*/
/* jn.c
Cephes Math Library Release 2.0: April, 1987
Copyright 1984, 1987 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#include <math.h>
extern long double MACHEPL;
#ifdef ANSIPROT
extern long double fabsl ( long double );
extern long double j0l ( long double );
extern long double j1l ( long double );
#else
long double fabsl(), j0l(), j1l();
#endif
long double jnl( n, x )
int n;
long double x;
{
long double pkm2, pkm1, pk, xk, r, ans;
int k, sign;
if( n < 0 )
{
n = -n;
if( (n & 1) == 0 ) /* -1**n */
sign = 1;
else
sign = -1;
}
else
sign = 1;
if( x < 0.0L )
{
if( n & 1 )
sign = -sign;
x = -x;
}
if( n == 0 )
return( sign * j0l(x) );
if( n == 1 )
return( sign * j1l(x) );
if( n == 2 )
return( sign * (2.0L * j1l(x) / x - j0l(x)) );
if( x < MACHEPL )
return( 0.0L );
/* continued fraction */
k = 53;
pk = 2 * (n + k);
ans = pk;
xk = x * x;
do
{
pk -= 2.0L;
ans = pk - (xk/ans);
}
while( --k > 0 );
ans = x/ans;
/* backward recurrence */
pk = 1.0L;
pkm1 = 1.0L/ans;
k = n-1;
r = 2 * k;
do
{
pkm2 = (pkm1 * r - pk * x) / x;
pk = pkm1;
pkm1 = pkm2;
r -= 2.0L;
}
while( --k > 0 );
if( fabsl(pk) > fabsl(pkm1) )
ans = j1l(x)/pk;
else
ans = j0l(x)/pkm1;
return( sign * ans );
}
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