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/* specfunc/gsl_sf_coulomb.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_COULOMB_H__
#define __GSL_SF_COULOMB_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
/* Normalized hydrogenic bound states, radial dependence. */
/* R_1 := 2Z sqrt(Z) exp(-Z r)
*/
int gsl_sf_hydrogenicR_1_e(const double Z, const double r, gsl_sf_result * result);
double gsl_sf_hydrogenicR_1(const double Z, const double r);
/* R_n := norm exp(-Z r/n) (2Z/n)^l Laguerre[n-l-1, 2l+1, 2Z/n r]
*
* normalization such that psi(n,l,r) = R_n Y_{lm}
*/
int gsl_sf_hydrogenicR_e(const int n, const int l, const double Z, const double r, gsl_sf_result * result);
double gsl_sf_hydrogenicR(const int n, const int l, const double Z, const double r);
/* Coulomb wave functions F_{lam_F}(eta,x), G_{lam_G}(eta,x)
* and their derivatives; lam_G := lam_F - k_lam_G
*
* lam_F, lam_G > -0.5
* x > 0.0
*
* Conventions of Abramowitz+Stegun.
*
* Because there can be a large dynamic range of values,
* overflows are handled gracefully. If an overflow occurs,
* GSL_EOVRFLW is signalled and exponent(s) are returned
* through exp_F, exp_G. These are such that
*
* F_L(eta,x) = fc[k_L] * exp(exp_F)
* G_L(eta,x) = gc[k_L] * exp(exp_G)
* F_L'(eta,x) = fcp[k_L] * exp(exp_F)
* G_L'(eta,x) = gcp[k_L] * exp(exp_G)
*/
int
gsl_sf_coulomb_wave_FG_e(const double eta, const double x,
const double lam_F,
const int k_lam_G,
gsl_sf_result * F, gsl_sf_result * Fp,
gsl_sf_result * G, gsl_sf_result * Gp,
double * exp_F, double * exp_G);
/* F_L(eta,x) as array */
int gsl_sf_coulomb_wave_F_array(
double lam_min, int kmax,
double eta, double x,
double * fc_array,
double * F_exponent
);
/* F_L(eta,x), G_L(eta,x) as arrays */
int gsl_sf_coulomb_wave_FG_array(double lam_min, int kmax,
double eta, double x,
double * fc_array, double * gc_array,
double * F_exponent,
double * G_exponent
);
/* F_L(eta,x), G_L(eta,x), F'_L(eta,x), G'_L(eta,x) as arrays */
int gsl_sf_coulomb_wave_FGp_array(double lam_min, int kmax,
double eta, double x,
double * fc_array, double * fcp_array,
double * gc_array, double * gcp_array,
double * F_exponent,
double * G_exponent
);
/* Coulomb wave function divided by the argument,
* F(eta, x)/x. This is the function which reduces to
* spherical Bessel functions in the limit eta->0.
*/
int gsl_sf_coulomb_wave_sphF_array(double lam_min, int kmax,
double eta, double x,
double * fc_array,
double * F_exponent
);
/* Coulomb wave function normalization constant.
* [Abramowitz+Stegun 14.1.8, 14.1.9]
*/
int gsl_sf_coulomb_CL_e(double L, double eta, gsl_sf_result * result);
int gsl_sf_coulomb_CL_array(double Lmin, int kmax, double eta, double * cl);
__END_DECLS
#endif /* __GSL_SF_COULOMB_H__ */
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