123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113 |
- /* 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 3 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_mode.h"
- #include "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__ */
|