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/* specfunc/gsl_sf_psi.h
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004 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 2 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_PSI_H__
#define __GSL_SF_PSI_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
/* Poly-Gamma Functions
*
* psi(m,x) := (d/dx)^m psi(0,x) = (d/dx)^{m+1} log(gamma(x))
*/
/* Di-Gamma Function psi(n) = psi(0,n)
*
* n > 0
* exceptions: GSL_EDOM
*/
int gsl_sf_psi_int_e(const int n, gsl_sf_result * result);
double gsl_sf_psi_int(const int n);
/* Di-Gamma Function psi(x) = psi(0, x)
*
* x != 0.0, -1.0, -2.0, ...
* exceptions: GSL_EDOM, GSL_ELOSS
*/
int gsl_sf_psi_e(const double x, gsl_sf_result * result);
double gsl_sf_psi(const double x);
/* Di-Gamma Function Re[psi(1 + I y)]
*
* exceptions: none
*/
int gsl_sf_psi_1piy_e(const double y, gsl_sf_result * result);
double gsl_sf_psi_1piy(const double y);
/* Di-Gamma Function psi(z) for general complex argument z = x + iy
*
* exceptions: GSL_EDOM
*/
int gsl_sf_complex_psi_e(
const double x,
const double y,
gsl_sf_result * result_re,
gsl_sf_result * result_im
);
/* Tri-Gamma Function psi^(1)(n)
*
* n > 0
* exceptions: GSL_EDOM
*/
int gsl_sf_psi_1_int_e(const int n, gsl_sf_result * result);
double gsl_sf_psi_1_int(const int n);
/* Tri-Gamma Function psi^(1)(x)
*
* x != 0.0, -1.0, -2.0, ...
* exceptions: GSL_EDOM, GSL_ELOSS
*/
int gsl_sf_psi_1_e(const double x, gsl_sf_result * result);
double gsl_sf_psi_1(const double x);
/* Poly-Gamma Function psi^(n)(x)
*
* n >= 0, x > 0.0
* exceptions: GSL_EDOM
*/
int gsl_sf_psi_n_e(const int n, const double x, gsl_sf_result * result);
double gsl_sf_psi_n(const int n, const double x);
__END_DECLS
#endif /* __GSL_SF_PSI_H__ */
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