include/gsl/gsl_sf_zeta.h

0001 /* specfunc/gsl_sf_zeta.h
0002  *
0003  * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004 Gerard Jungman
0004  *
0005  * This program is free software; you can redistribute it and/or modify
0006  * it under the terms of the GNU General Public License as published by
0007  * the Free Software Foundation; either version 3 of the License, or (at
0008  * your option) any later version.
0009  *
0010  * This program is distributed in the hope that it will be useful, but
0011  * WITHOUT ANY WARRANTY; without even the implied warranty of
0012  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0013  * General Public License for more details.
0014  *
0015  * You should have received a copy of the GNU General Public License
0016  * along with this program; if not, write to the Free Software
0017  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
0018  */
0019
0020 /* Author:  G. Jungman */
0021
0022 #ifndef __GSL_SF_ZETA_H__
0023 #define __GSL_SF_ZETA_H__
0024
0025 #include <gsl/gsl_sf_result.h>
0026
0027 #undef __BEGIN_DECLS
0028 #undef __END_DECLS
0029 #ifdef __cplusplus
0030 # define __BEGIN_DECLS extern "C" {
0031 # define __END_DECLS }
0032 #else
0033 # define __BEGIN_DECLS /* empty */
0034 # define __END_DECLS /* empty */
0035 #endif
0036
0037 __BEGIN_DECLS
0038
0039
0040 /* Riemann Zeta Function
0041  * zeta(n) = Sum[ k^(-n), {k,1,Infinity} ]
0042  *
0043  * n=integer, n != 1
0044  * exceptions: GSL_EDOM, GSL_EOVRFLW
0045  */
0046 int gsl_sf_zeta_int_e(const int n, gsl_sf_result * result);
0047 double gsl_sf_zeta_int(const int n);
0048
0049
0050 /* Riemann Zeta Function
0051  * zeta(x) = Sum[ k^(-s), {k,1,Infinity} ], s != 1.0
0052  *
0053  * s != 1.0
0054  * exceptions: GSL_EDOM, GSL_EOVRFLW
0055  */
0056 int gsl_sf_zeta_e(const double s, gsl_sf_result * result);
0057 double gsl_sf_zeta(const double s);
0058
0059
0060 /* Riemann Zeta Function minus 1
0061  *   useful for evaluating the fractional part
0062  *   of Riemann zeta for large argument
0063  *
0064  * s != 1.0
0065  * exceptions: GSL_EDOM, GSL_EOVRFLW
0066  */
0067 int gsl_sf_zetam1_e(const double s, gsl_sf_result * result);
0068 double gsl_sf_zetam1(const double s);
0069
0070
0071 /* Riemann Zeta Function minus 1 for integer arg
0072  *   useful for evaluating the fractional part
0073  *   of Riemann zeta for large argument
0074  *
0075  * s != 1.0
0076  * exceptions: GSL_EDOM, GSL_EOVRFLW
0077  */
0078 int gsl_sf_zetam1_int_e(const int s, gsl_sf_result * result);
0079 double gsl_sf_zetam1_int(const int s);
0080
0081
0082 /* Hurwitz Zeta Function
0083  * zeta(s,q) = Sum[ (k+q)^(-s), {k,0,Infinity} ]
0084  *
0085  * s > 1.0, q > 0.0
0086  * exceptions: GSL_EDOM, GSL_EUNDRFLW, GSL_EOVRFLW
0087  */
0088 int gsl_sf_hzeta_e(const double s, const double q, gsl_sf_result * result);
0089 double gsl_sf_hzeta(const double s, const double q);
0090
0091
0092 /* Eta Function
0093  * eta(n) = (1-2^(1-n)) zeta(n)
0094  *
0095  * exceptions: GSL_EUNDRFLW, GSL_EOVRFLW
0096  */
0097 int gsl_sf_eta_int_e(int n, gsl_sf_result * result);
0098 double gsl_sf_eta_int(const int n);
0099
0100
0101 /* Eta Function
0102  * eta(s) = (1-2^(1-s)) zeta(s)
0103  *
0104  * exceptions: GSL_EUNDRFLW, GSL_EOVRFLW
0105  */
0106 int gsl_sf_eta_e(const double s, gsl_sf_result * result);
0107 double gsl_sf_eta(const double s);
0108
0109
0110 __END_DECLS
0111
0112 #endif /* __GSL_SF_ZETA_H__ */