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/* yn.c
*
* Bessel function of second kind of integer order
*
*
*
* SYNOPSIS:
*
* double x, y, yn();
* int n;
*
* y = yn( n, x );
*
*
*
* DESCRIPTION:
*
* Returns Bessel function of order n, where n is a
* (possibly negative) integer.
*
* The function is evaluated by forward recurrence on
* n, starting with values computed by the routines
* y0() and y1().
*
* If n = 0 or 1 the routine for y0 or y1 is called
* directly.
*
*
*
* ACCURACY:
*
*
* Absolute error, except relative
* when y > 1:
* arithmetic domain # trials peak rms
* DEC 0, 30 2200 2.9e-16 5.3e-17
* IEEE 0, 30 30000 3.4e-15 4.3e-16
*
*
* ERROR MESSAGES:
*
* message condition value returned
* yn singularity x = 0 MAXNUM
* yn overflow MAXNUM
*
* Spot checked against tables for x, n between 0 and 100.
*
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
extern double MAXNUM, MAXLOG;
double yn( n, x )
int n;
double x;
{
double an, anm1, anm2, r;
int k, sign;
if( n < 0 )
{
n = -n;
if( (n & 1) == 0 ) /* -1**n */
sign = 1;
else
sign = -1;
}
else
sign = 1;
if( n == 0 )
return( sign * y0(x) );
if( n == 1 )
return( sign * y1(x) );
/* test for overflow */
if (x == 0.0) {
mtherr("yn", SING);
return -NPY_INFINITY;
} else if (x < 0.0) {
mtherr("yn", DOMAIN);
return NPY_NAN;
}
/* forward recurrence on n */
anm2 = y0(x);
anm1 = y1(x);
k = 1;
r = 2 * k;
do
{
an = r * anm1 / x - anm2;
anm2 = anm1;
anm1 = an;
r += 2.0;
++k;
}
while( k < n );
return( sign * an );
}
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