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/* 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 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_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__ */
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