| /* specfunc/gsl_sf_ellint.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 __GSL_SF_ELLINT_H__ |
| #define __GSL_SF_ELLINT_H__ |
| |
| #include <gsl/gsl_mode.h> |
| #include <gsl/gsl_sf_result.h> |
| |
| #undef __BEGIN_DECLS |
| #undef __END_DECLS |
| #ifdef __cplusplus |
| # define __BEGIN_DECLS extern "C" { |
| # define __END_DECLS } |
| #else |
| # define __BEGIN_DECLS /* empty */ |
| # define __END_DECLS /* empty */ |
| #endif |
| |
| __BEGIN_DECLS |
| |
| |
| /* Legendre form of complete elliptic integrals |
| * |
| * K(k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}] |
| * E(k) = Integral[ Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}] |
| * |
| * exceptions: GSL_EDOM |
| */ |
| int gsl_sf_ellint_Kcomp_e(double k, gsl_mode_t mode, gsl_sf_result * result); |
| double gsl_sf_ellint_Kcomp(double k, gsl_mode_t mode); |
| |
| int gsl_sf_ellint_Ecomp_e(double k, gsl_mode_t mode, gsl_sf_result * result); |
| double gsl_sf_ellint_Ecomp(double k, gsl_mode_t mode); |
| |
| int gsl_sf_ellint_Pcomp_e(double k, double n, gsl_mode_t mode, gsl_sf_result * result); |
| double gsl_sf_ellint_Pcomp(double k, double n, gsl_mode_t mode); |
| |
| int gsl_sf_ellint_Dcomp_e(double k, gsl_mode_t mode, gsl_sf_result * result); |
| double gsl_sf_ellint_Dcomp(double k, gsl_mode_t mode); |
| |
| |
| /* Legendre form of incomplete elliptic integrals |
| * |
| * F(phi,k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}] |
| * E(phi,k) = Integral[ Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}] |
| * P(phi,k,n) = Integral[(1 + n Sin[t]^2)^(-1)/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}] |
| * D(phi,k,n) = R_D(1-Sin[phi]^2, 1-k^2 Sin[phi]^2, 1.0) |
| * |
| * F: [Carlson, Numerische Mathematik 33 (1979) 1, (4.1)] |
| * E: [Carlson, ", (4.2)] |
| * P: [Carlson, ", (4.3)] |
| * D: [Carlson, ", (4.4)] |
| * |
| * exceptions: GSL_EDOM |
| */ |
| int gsl_sf_ellint_F_e(double phi, double k, gsl_mode_t mode, gsl_sf_result * result); |
| double gsl_sf_ellint_F(double phi, double k, gsl_mode_t mode); |
| |
| int gsl_sf_ellint_E_e(double phi, double k, gsl_mode_t mode, gsl_sf_result * result); |
| double gsl_sf_ellint_E(double phi, double k, gsl_mode_t mode); |
| |
| int gsl_sf_ellint_P_e(double phi, double k, double n, gsl_mode_t mode, gsl_sf_result * result); |
| double gsl_sf_ellint_P(double phi, double k, double n, gsl_mode_t mode); |
| |
| int gsl_sf_ellint_D_e(double phi, double k, double n, gsl_mode_t mode, gsl_sf_result * result); |
| double gsl_sf_ellint_D(double phi, double k, double n, gsl_mode_t mode); |
| |
| |
| /* Carlson's symmetric basis of functions |
| * |
| * RC(x,y) = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1)], {t,0,Inf}] |
| * RD(x,y,z) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-3/2), {t,0,Inf}] |
| * RF(x,y,z) = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2), {t,0,Inf}] |
| * RJ(x,y,z,p) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2) (t+p)^(-1), {t,0,Inf}] |
| * |
| * exceptions: GSL_EDOM |
| */ |
| int gsl_sf_ellint_RC_e(double x, double y, gsl_mode_t mode, gsl_sf_result * result); |
| double gsl_sf_ellint_RC(double x, double y, gsl_mode_t mode); |
| |
| int gsl_sf_ellint_RD_e(double x, double y, double z, gsl_mode_t mode, gsl_sf_result * result); |
| double gsl_sf_ellint_RD(double x, double y, double z, gsl_mode_t mode); |
| |
| int gsl_sf_ellint_RF_e(double x, double y, double z, gsl_mode_t mode, gsl_sf_result * result); |
| double gsl_sf_ellint_RF(double x, double y, double z, gsl_mode_t mode); |
| |
| int gsl_sf_ellint_RJ_e(double x, double y, double z, double p, gsl_mode_t mode, gsl_sf_result * result); |
| double gsl_sf_ellint_RJ(double x, double y, double z, double p, gsl_mode_t mode); |
| |
| |
| __END_DECLS |
| |
| #endif /* __GSL_SF_ELLINT_H__ */ |