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/* specfunc/gsl_sf_coulomb.h
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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/* Author: G. Jungman */
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#ifndef __GSL_SF_COULOMB_H__
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#define __GSL_SF_COULOMB_H__
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#include <gsl/gsl_mode.h>
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#include <gsl/gsl_sf_result.h>
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#undef __BEGIN_DECLS
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#undef __END_DECLS
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#ifdef __cplusplus
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# define __BEGIN_DECLS extern "C" {
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# define __END_DECLS }
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#else
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# define __BEGIN_DECLS /* empty */
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# define __END_DECLS /* empty */
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#endif
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__BEGIN_DECLS
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/* Normalized hydrogenic bound states, radial dependence. */
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/* R_1 := 2Z sqrt(Z) exp(-Z r)
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*/
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int gsl_sf_hydrogenicR_1_e(const double Z, const double r, gsl_sf_result * result);
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double gsl_sf_hydrogenicR_1(const double Z, const double r);
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/* R_n := norm exp(-Z r/n) (2Z/n)^l Laguerre[n-l-1, 2l+1, 2Z/n r]
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*
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* normalization such that psi(n,l,r) = R_n Y_{lm}
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*/
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int gsl_sf_hydrogenicR_e(const int n, const int l, const double Z, const double r, gsl_sf_result * result);
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double gsl_sf_hydrogenicR(const int n, const int l, const double Z, const double r);
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/* Coulomb wave functions F_{lam_F}(eta,x), G_{lam_G}(eta,x)
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* and their derivatives; lam_G := lam_F - k_lam_G
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*
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* lam_F, lam_G > -0.5
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* x > 0.0
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*
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* Conventions of Abramowitz+Stegun.
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*
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* Because there can be a large dynamic range of values,
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* overflows are handled gracefully. If an overflow occurs,
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* GSL_EOVRFLW is signalled and exponent(s) are returned
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* through exp_F, exp_G. These are such that
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*
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* F_L(eta,x) = fc[k_L] * exp(exp_F)
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* G_L(eta,x) = gc[k_L] * exp(exp_G)
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* F_L'(eta,x) = fcp[k_L] * exp(exp_F)
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* G_L'(eta,x) = gcp[k_L] * exp(exp_G)
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*/
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int
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gsl_sf_coulomb_wave_FG_e(const double eta, const double x,
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const double lam_F,
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const int k_lam_G,
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gsl_sf_result * F, gsl_sf_result * Fp,
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gsl_sf_result * G, gsl_sf_result * Gp,
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double * exp_F, double * exp_G);
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/* F_L(eta,x) as array */
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int gsl_sf_coulomb_wave_F_array(
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double lam_min, int kmax,
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double eta, double x,
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double * fc_array,
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double * F_exponent
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);
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/* F_L(eta,x), G_L(eta,x) as arrays */
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int gsl_sf_coulomb_wave_FG_array(double lam_min, int kmax,
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double eta, double x,
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double * fc_array, double * gc_array,
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double * F_exponent,
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double * G_exponent
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);
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/* F_L(eta,x), G_L(eta,x), F'_L(eta,x), G'_L(eta,x) as arrays */
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int gsl_sf_coulomb_wave_FGp_array(double lam_min, int kmax,
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double eta, double x,
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double * fc_array, double * fcp_array,
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double * gc_array, double * gcp_array,
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double * F_exponent,
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double * G_exponent
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);
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/* Coulomb wave function divided by the argument,
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* F(eta, x)/x. This is the function which reduces to
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* spherical Bessel functions in the limit eta->0.
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*/
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int gsl_sf_coulomb_wave_sphF_array(double lam_min, int kmax,
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double eta, double x,
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double * fc_array,
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double * F_exponent
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);
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/* Coulomb wave function normalization constant.
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* [Abramowitz+Stegun 14.1.8, 14.1.9]
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*/
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int gsl_sf_coulomb_CL_e(double L, double eta, gsl_sf_result * result);
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int gsl_sf_coulomb_CL_array(double Lmin, int kmax, double eta, double * cl);
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__END_DECLS
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#endif /* __GSL_SF_COULOMB_H__ */
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