1 /** @file inifcns_zeta.cpp
3 * Implementation of the Zeta-function and some related stuff. */
6 * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
18 * You should have received a copy of the GNU General Public License
19 * along with this program; if not, write to the Free Software
20 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
34 #ifndef NO_GINAC_NAMESPACE
36 #endif // ndef NO_GINAC_NAMESPACE
39 // Riemann's Zeta-function
42 static ex zeta1_evalf(const ex & x)
46 END_TYPECHECK(zeta(x))
48 return zeta(ex_to_numeric(x));
51 static ex zeta1_eval(const ex & x)
53 if (x.info(info_flags::numeric)) {
54 numeric y = ex_to_numeric(x);
55 // trap integer arguments:
59 if (x.is_equal(_ex1()))
60 throw(std::domain_error("zeta(1): infinity"));
61 if (x.info(info_flags::posint)) {
62 if (x.info(info_flags::odd))
63 return zeta(x).hold();
65 return abs(bernoulli(y))*pow(Pi,x)*pow(_num2(),y-_num1())/factorial(y);
67 if (x.info(info_flags::odd))
68 return -bernoulli(_num1()-y)/(_num1()-y);
74 return zeta(x).hold();
77 static ex zeta1_diff(const ex & x, unsigned diff_param)
79 GINAC_ASSERT(diff_param==0);
81 return zeta(_ex1(), x);
84 const unsigned function_index_zeta1 = function::register_new("zeta", zeta1_eval, zeta1_evalf, zeta1_diff, NULL);
87 // Derivatives of Riemann's Zeta-function zeta(0,x)==zeta(x)
90 static ex zeta2_eval(const ex & n, const ex & x)
92 if (n.info(info_flags::numeric)) {
93 // zeta(0,x) -> zeta(x)
98 return zeta(n, x).hold();
101 static ex zeta2_diff(const ex & n, const ex & x, unsigned diff_param)
103 GINAC_ASSERT(diff_param<2);
107 throw(std::logic_error("cannot diff zeta(n,x) with respect to n"));
113 const unsigned function_index_zeta2 = function::register_new("zeta", zeta2_eval, NULL, zeta2_diff, NULL);
115 #ifndef NO_GINAC_NAMESPACE
117 #endif // ndef NO_GINAC_NAMESPACE