/* 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__ */