/* specfunc/gsl_sf_zeta.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_ZETA_H__

#define __GSL_SF_ZETA_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

/* Riemann Zeta Function

 * zeta(n) = Sum[ k^(-n), {k,1,Infinity} ]

 *

 * n=integer, n != 1

 * exceptions: GSL_EDOM, GSL_EOVRFLW

 */

int gsl_sf_zeta_int_e(const int n, gsl_sf_result * result);

double gsl_sf_zeta_int(const int n);

/* Riemann Zeta Function

 * zeta(x) = Sum[ k^(-s), {k,1,Infinity} ], s != 1.0

 *

 * s != 1.0

 * exceptions: GSL_EDOM, GSL_EOVRFLW

 */

int gsl_sf_zeta_e(const double s, gsl_sf_result * result);

double gsl_sf_zeta(const double s);

/* Riemann Zeta Function minus 1

 *   useful for evaluating the fractional part

 *   of Riemann zeta for large argument

 *

 * s != 1.0

 * exceptions: GSL_EDOM, GSL_EOVRFLW

 */

int gsl_sf_zetam1_e(const double s, gsl_sf_result * result);

double gsl_sf_zetam1(const double s);

/* Riemann Zeta Function minus 1 for integer arg

 *   useful for evaluating the fractional part

 *   of Riemann zeta for large argument

 *

 * s != 1.0

 * exceptions: GSL_EDOM, GSL_EOVRFLW

 */

int gsl_sf_zetam1_int_e(const int s, gsl_sf_result * result);

double gsl_sf_zetam1_int(const int s);

/* Hurwitz Zeta Function

 * zeta(s,q) = Sum[ (k+q)^(-s), {k,0,Infinity} ]

 *

 * s > 1.0, q > 0.0

 * exceptions: GSL_EDOM, GSL_EUNDRFLW, GSL_EOVRFLW

 */

int gsl_sf_hzeta_e(const double s, const double q, gsl_sf_result * result);

double gsl_sf_hzeta(const double s, const double q);

/* Eta Function

 * eta(n) = (1-2^(1-n)) zeta(n)

 *

 * exceptions: GSL_EUNDRFLW, GSL_EOVRFLW

 */

int gsl_sf_eta_int_e(int n, gsl_sf_result * result);

double gsl_sf_eta_int(const int n);

/* Eta Function

 * eta(s) = (1-2^(1-s)) zeta(s)

 *

 * exceptions: GSL_EUNDRFLW, GSL_EOVRFLW

 */

int gsl_sf_eta_e(const double s, gsl_sf_result * result);

double gsl_sf_eta(const double s);

__END_DECLS

#endif /* __GSL_SF_ZETA_H__ */