1/* specfunc/gsl_sf_zeta.h
2 *
3 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004 Gerard Jungman
4 *
5 * This program is free software; you can redistribute it and/or modify
6 * it under the terms of the GNU General Public License as published by
7 * the Free Software Foundation; either version 3 of the License, or (at
8 * your option) any later version.
9 *
10 * This program is distributed in the hope that it will be useful, but
11 * WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * General Public License for more details.
14 *
15 * You should have received a copy of the GNU General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
18 */
19
20/* Author: G. Jungman */
21
22#ifndef __GSL_SF_ZETA_H__
23#define __GSL_SF_ZETA_H__
24
25#include <gsl/gsl_sf_result.h>
26
27#undef __BEGIN_DECLS
28#undef __END_DECLS
29#ifdef __cplusplus
30# define __BEGIN_DECLS extern "C" {
31# define __END_DECLS }
32#else
33# define __BEGIN_DECLS /* empty */
34# define __END_DECLS /* empty */
35#endif
36
37__BEGIN_DECLS
38
39
40/* Riemann Zeta Function
41 * zeta(n) = Sum[ k^(-n), {k,1,Infinity} ]
42 *
43 * n=integer, n != 1
44 * exceptions: GSL_EDOM, GSL_EOVRFLW
45 */
46int gsl_sf_zeta_int_e(const int n, gsl_sf_result * result);
47double gsl_sf_zeta_int(const int n);
48
49
50/* Riemann Zeta Function
51 * zeta(x) = Sum[ k^(-s), {k,1,Infinity} ], s != 1.0
52 *
53 * s != 1.0
54 * exceptions: GSL_EDOM, GSL_EOVRFLW
55 */
56int gsl_sf_zeta_e(const double s, gsl_sf_result * result);
57double gsl_sf_zeta(const double s);
58
59
60/* Riemann Zeta Function minus 1
61 * useful for evaluating the fractional part
62 * of Riemann zeta for large argument
63 *
64 * s != 1.0
65 * exceptions: GSL_EDOM, GSL_EOVRFLW
66 */
67int gsl_sf_zetam1_e(const double s, gsl_sf_result * result);
68double gsl_sf_zetam1(const double s);
69
70
71/* Riemann Zeta Function minus 1 for integer arg
72 * useful for evaluating the fractional part
73 * of Riemann zeta for large argument
74 *
75 * s != 1.0
76 * exceptions: GSL_EDOM, GSL_EOVRFLW
77 */
78int gsl_sf_zetam1_int_e(const int s, gsl_sf_result * result);
79double gsl_sf_zetam1_int(const int s);
80
81
82/* Hurwitz Zeta Function
83 * zeta(s,q) = Sum[ (k+q)^(-s), {k,0,Infinity} ]
84 *
85 * s > 1.0, q > 0.0
86 * exceptions: GSL_EDOM, GSL_EUNDRFLW, GSL_EOVRFLW
87 */
88int gsl_sf_hzeta_e(const double s, const double q, gsl_sf_result * result);
89double gsl_sf_hzeta(const double s, const double q);
90
91
92/* Eta Function
93 * eta(n) = (1-2^(1-n)) zeta(n)
94 *
95 * exceptions: GSL_EUNDRFLW, GSL_EOVRFLW
96 */
97int gsl_sf_eta_int_e(int n, gsl_sf_result * result);
98double gsl_sf_eta_int(const int n);
99
100
101/* Eta Function
102 * eta(s) = (1-2^(1-s)) zeta(s)
103 *
104 * exceptions: GSL_EUNDRFLW, GSL_EOVRFLW
105 */
106int gsl_sf_eta_e(const double s, gsl_sf_result * result);
107double gsl_sf_eta(const double s);
108
109
110__END_DECLS
111
112#endif /* __GSL_SF_ZETA_H__ */
113