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yn.c

/*                                        yn.c
 *
 *    Bessel function of second kind of integer order
 *
 *
 *
 * SYNOPSIS:
 *
 * double y = yn (int n, double 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"

double cephes_bessel_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) {
      mtherr("yn", CEPHES_SING);
      return -MAXNUM;
    }

    /* 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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