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/* specfunc/gsl_sf_mathieu.h
*
* Copyright (C) 2002 Lowell Johnson
*
* 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., 675 Mass Ave, Cambridge, MA 02139, USA.
*/
/* Author: L. Johnson */
#ifndef __GSL_SF_MATHIEU_H__
#define __GSL_SF_MATHIEU_H__
#include <gsl/gsl_sf_result.h>
#include <gsl/gsl_eigen.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
#define GSL_SF_MATHIEU_COEFF 100
typedef struct
{
size_t size;
size_t even_order;
size_t odd_order;
int extra_values;
double qa; /* allow for caching of results: not implemented yet */
double qb; /* allow for caching of results: not implemented yet */
double *aa;
double *bb;
double *dd;
double *ee;
double *tt;
double *e2;
double *zz;
gsl_vector *eval;
gsl_matrix *evec;
gsl_eigen_symmv_workspace *wmat;
} gsl_sf_mathieu_workspace;
/* Compute an array of characteristic (eigen) values from the recurrence
matrices for the Mathieu equations. */
int gsl_sf_mathieu_a_array(int order_min, int order_max, double qq, gsl_sf_mathieu_workspace *work, double result_array[]);
int gsl_sf_mathieu_b_array(int order_min, int order_max, double qq, gsl_sf_mathieu_workspace *work, double result_array[]);
/* Compute the characteristic value for a Mathieu function of order n and
type ntype. */
int gsl_sf_mathieu_a_e(int order, double qq, gsl_sf_result *result);
double gsl_sf_mathieu_a(int order, double qq);
int gsl_sf_mathieu_b_e(int order, double qq, gsl_sf_result *result);
double gsl_sf_mathieu_b(int order, double qq);
/* Compute the Fourier coefficients for a Mathieu function. */
int gsl_sf_mathieu_a_coeff(int order, double qq, double aa, double coeff[]);
int gsl_sf_mathieu_b_coeff(int order, double qq, double aa, double coeff[]);
/* Allocate computational storage space for eigenvalue solution. */
gsl_sf_mathieu_workspace *gsl_sf_mathieu_alloc(const size_t nn,
const double qq);
void gsl_sf_mathieu_free(gsl_sf_mathieu_workspace *workspace);
/* Compute an angular Mathieu function. */
int gsl_sf_mathieu_ce_e(int order, double qq, double zz, gsl_sf_result *result);
double gsl_sf_mathieu_ce(int order, double qq, double zz);
int gsl_sf_mathieu_se_e(int order, double qq, double zz, gsl_sf_result *result);
double gsl_sf_mathieu_se(int order, double qq, double zz);
int gsl_sf_mathieu_ce_array(int nmin, int nmax, double qq, double zz,
gsl_sf_mathieu_workspace *work,
double result_array[]);
int gsl_sf_mathieu_se_array(int nmin, int nmax, double qq, double zz,
gsl_sf_mathieu_workspace *work,
double result_array[]);
/* Compute a radial Mathieu function. */
int gsl_sf_mathieu_Mc_e(int kind, int order, double qq, double zz,
gsl_sf_result *result);
double gsl_sf_mathieu_Mc(int kind, int order, double qq, double zz);
int gsl_sf_mathieu_Ms_e(int kind, int order, double qq, double zz,
gsl_sf_result *result);
double gsl_sf_mathieu_Ms(int kind, int order, double qq, double zz);
int gsl_sf_mathieu_Mc_array(int kind, int nmin, int nmax, double qq,
double zz, gsl_sf_mathieu_workspace *work,
double result_array[]);
int gsl_sf_mathieu_Ms_array(int kind, int nmin, int nmax, double qq,
double zz, gsl_sf_mathieu_workspace *work,
double result_array[]);
__END_DECLS
#endif /* !__GSL_SF_MATHIEU_H__ */
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