yn.c

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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
 *    IEEE      0, 30       30000       3.4e-15     4.3e-16
 *
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * yn singularity   x = 0              INFINITY
 * yn overflow                         INFINITY
 *
 * 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 MAXLOG;
 
double yn(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) {
        sf_error("yn", SF_ERROR_SINGULAR, NULL);
        return -INFINITY * sign;
    }
    else if (x < 0.0) {
        sf_error("yn", SF_ERROR_DOMAIN, NULL);
        return 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);
}