/* 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 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_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__ */