| /* specfunc/bessel.h |
| * |
| * 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 */ |
| |
| #ifndef _BESSEL_H_ |
| #define _BESSEL_H_ |
| |
| #include <gsl/gsl_sf_result.h> |
| |
| |
| /* Taylor expansion for J_nu(x) or I_nu(x) |
| * sign = -1 ==> Jnu |
| * sign = +1 ==> Inu |
| */ |
| int gsl_sf_bessel_IJ_taylor_e(const double nu, const double x, |
| const int sign, |
| const int kmax, |
| const double threshold, |
| gsl_sf_result * result |
| ); |
| |
| int gsl_sf_bessel_Jnu_asympx_e(const double nu, const double x, gsl_sf_result * result); |
| int gsl_sf_bessel_Ynu_asympx_e(const double nu, const double x, gsl_sf_result * result); |
| |
| int gsl_sf_bessel_Inu_scaled_asympx_e(const double nu, const double x, gsl_sf_result * result); |
| int gsl_sf_bessel_Knu_scaled_asympx_e(const double nu, const double x, gsl_sf_result * result); |
| |
| int gsl_sf_bessel_Inu_scaled_asymp_unif_e(const double nu, const double x, gsl_sf_result * result); |
| int gsl_sf_bessel_Knu_scaled_asymp_unif_e(const double nu, const double x, gsl_sf_result * result); |
| |
| |
| /* ratio = J_{nu+1}(x) / J_nu(x) |
| * sgn = sgn(J_nu(x)) |
| */ |
| int |
| gsl_sf_bessel_J_CF1(const double nu, const double x, double * ratio, double * sgn); |
| |
| |
| /* ratio = I_{nu+1}(x) / I_nu(x) |
| */ |
| int |
| gsl_sf_bessel_I_CF1_ser(const double nu, const double x, double * ratio); |
| |
| |
| /* Evaluate the Steed method continued fraction CF2 for |
| * |
| * (J' + i Y')/(J + i Y) := P + i Q |
| */ |
| int |
| gsl_sf_bessel_JY_steed_CF2(const double nu, const double x, |
| double * P, double * Q); |
| |
| |
| int |
| gsl_sf_bessel_JY_mu_restricted(const double mu, const double x, |
| gsl_sf_result * Jmu, gsl_sf_result * Jmup1, |
| gsl_sf_result * Ymu, gsl_sf_result * Ymup1); |
| |
| |
| int |
| gsl_sf_bessel_K_scaled_steed_temme_CF2(const double nu, const double x, |
| double * K_nu, double * K_nup1, |
| double * Kp_nu); |
| |
| |
| /* These are of use in calculating the oscillating |
| * Bessel functions. |
| * cos(y - pi/4 + eps) |
| * sin(y - pi/4 + eps) |
| */ |
| int gsl_sf_bessel_cos_pi4_e(double y, double eps, gsl_sf_result * result); |
| int gsl_sf_bessel_sin_pi4_e(double y, double eps, gsl_sf_result * result); |
| |
| |
| #endif /* !_BESSEL_H_ */ |
