| /* specfunc/bessel_Ynu.c |
| * |
| * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman |
| * |
| * This program is free software; you can redistribute it and/or modify |
| * it under the terms of the GNU General Public License as published by |
| * the Free Software Foundation; either version 2 of the License, or (at |
| * your option) any later version. |
| * |
| * This program is distributed in the hope that it will be useful, but |
| * WITHOUT ANY WARRANTY; without even the implied warranty of |
| * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| * General Public License for more details. |
| * |
| * You should have received a copy of the GNU General Public License |
| * along with this program; if not, write to the Free Software |
| * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. |
| */ |
| |
| /* Author: G. Jungman */ |
| |
| #include <config.h> |
| #include <gsl/gsl_math.h> |
| #include <gsl/gsl_errno.h> |
| #include <gsl/gsl_sf_bessel.h> |
| |
| #include "error.h" |
| |
| #include "bessel.h" |
| #include "bessel_olver.h" |
| #include "bessel_temme.h" |
| |
| /* Perform forward recurrence for Y_nu(x) and Y'_nu(x) |
| * |
| * Y_{nu+1} = nu/x Y_nu - Y'_nu |
| * Y'_{nu+1} = -(nu+1)/x Y_{nu+1} + Y_nu |
| */ |
| #if 0 |
| static |
| int |
| bessel_Y_recur(const double nu_min, const double x, const int kmax, |
| const double Y_start, const double Yp_start, |
| double * Y_end, double * Yp_end) |
| { |
| double x_inv = 1.0/x; |
| double nu = nu_min; |
| double Y_nu = Y_start; |
| double Yp_nu = Yp_start; |
| int k; |
| |
| for(k=1; k<=kmax; k++) { |
| double nuox = nu*x_inv; |
| double Y_nu_save = Y_nu; |
| Y_nu = -Yp_nu + nuox * Y_nu; |
| Yp_nu = Y_nu_save - (nuox+x_inv) * Y_nu; |
| nu += 1.0; |
| } |
| *Y_end = Y_nu; |
| *Yp_end = Yp_nu; |
| return GSL_SUCCESS; |
| } |
| #endif |
| |
| |
| /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/ |
| |
| int |
| gsl_sf_bessel_Ynu_e(double nu, double x, gsl_sf_result * result) |
| { |
| /* CHECK_POINTER(result) */ |
| |
| if(x <= 0.0 || nu < 0.0) { |
| DOMAIN_ERROR(result); |
| } |
| else if(nu > 50.0) { |
| return gsl_sf_bessel_Ynu_asymp_Olver_e(nu, x, result); |
| } |
| else { |
| /* -1/2 <= mu <= 1/2 */ |
| int N = (int)(nu + 0.5); |
| double mu = nu - N; |
| |
| gsl_sf_result Y_mu, Y_mup1; |
| int stat_mu; |
| double Ynm1; |
| double Yn; |
| double Ynp1; |
| int n; |
| |
| if(x < 2.0) { |
| /* Determine Ymu, Ymup1 directly. This is really |
| * an optimization since this case could as well |
| * be handled by a call to gsl_sf_bessel_JY_mu_restricted(), |
| * as below. |
| */ |
| stat_mu = gsl_sf_bessel_Y_temme(mu, x, &Y_mu, &Y_mup1); |
| } |
| else { |
| /* Determine Ymu, Ymup1 and Jmu, Jmup1. |
| */ |
| gsl_sf_result J_mu, J_mup1; |
| stat_mu = gsl_sf_bessel_JY_mu_restricted(mu, x, &J_mu, &J_mup1, &Y_mu, &Y_mup1); |
| } |
| |
| /* Forward recursion to get Ynu, Ynup1. |
| */ |
| Ynm1 = Y_mu.val; |
| Yn = Y_mup1.val; |
| for(n=1; n<=N; n++) { |
| Ynp1 = 2.0*(mu+n)/x * Yn - Ynm1; |
| Ynm1 = Yn; |
| Yn = Ynp1; |
| } |
| |
| result->val = Ynm1; /* Y_nu */ |
| result->err = (N + 1.0) * fabs(Ynm1) * (fabs(Y_mu.err/Y_mu.val) + fabs(Y_mup1.err/Y_mup1.val)); |
| result->err += 2.0 * GSL_DBL_EPSILON * fabs(Ynm1); |
| |
| return stat_mu; |
| } |
| } |
| |
| |
| /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ |
| |
| #include "eval.h" |
| |
| double gsl_sf_bessel_Ynu(const double nu, const double x) |
| { |
| EVAL_RESULT(gsl_sf_bessel_Ynu_e(nu, x, &result)); |
| } |