1 /** @file inifcns_zeta.cpp
3 * Implementation of the Zeta-function and some related stuff. */
6 * GiNaC Copyright (C) 1999-2003 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
31 #include "operators.h"
37 // Riemann's Zeta-function
40 static ex zeta1_evalf(const ex & x)
42 if (is_exactly_a<numeric>(x)) {
44 return zeta(ex_to<numeric>(x));
45 } catch (const dunno &e) { }
48 return zeta(x).hold();
51 static ex zeta1_eval(const ex & x)
53 if (x.info(info_flags::numeric)) {
54 const numeric &y = ex_to<numeric>(x);
55 // trap integer arguments:
59 if (y.is_equal(_num1))
60 throw(std::domain_error("zeta(1): infinity"));
61 if (y.info(info_flags::posint)) {
62 if (y.info(info_flags::odd))
63 return zeta(x).hold();
65 return abs(bernoulli(y))*pow(Pi,y)*pow(_num2,y-_num1)/factorial(y);
67 if (y.info(info_flags::odd))
68 return -bernoulli(_num1-y)/(_num1-y);
74 if (y.info(info_flags::numeric) && !y.info(info_flags::crational))
75 return zeta1_evalf(x);
77 return zeta(x).hold();
80 static ex zeta1_deriv(const ex & x, unsigned deriv_param)
82 GINAC_ASSERT(deriv_param==0);
87 unsigned zeta1_SERIAL::serial =
88 function::register_new(function_options("zeta").
89 eval_func(zeta1_eval).
90 evalf_func(zeta1_evalf).
91 derivative_func(zeta1_deriv).
96 // Derivatives of Riemann's Zeta-function zeta(0,x)==zeta(x)
99 static ex zeta2_eval(const ex & n, const ex & x)
101 if (n.info(info_flags::numeric)) {
102 // zeta(0,x) -> zeta(x)
107 return zeta(n, x).hold();
110 static ex zeta2_deriv(const ex & n, const ex & x, unsigned deriv_param)
112 GINAC_ASSERT(deriv_param<2);
114 if (deriv_param==0) {
116 throw(std::logic_error("cannot diff zeta(n,x) with respect to n"));
122 unsigned zeta2_SERIAL::serial =
123 function::register_new(function_options("zeta").
124 eval_func(zeta2_eval).
125 derivative_func(zeta2_deriv).
126 latex_name("\\zeta").