1 /** @file inifcns_zeta.cpp
3 * Implementation of the Zeta-function and some related stuff. */
6 * GiNaC Copyright (C) 1999 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
36 // Riemann's Zeta-function
39 static ex zeta_eval(ex const & x)
41 if (x.info(info_flags::numeric)) {
42 // trap integer arguments:
43 if (x.info(info_flags::integer)) {
46 if (!x.compare(exONE()))
47 throw(std::domain_error("zeta(1): infinity"));
48 if (x.info(info_flags::posint)) {
49 if (x.info(info_flags::odd))
50 return zeta(x).hold();
52 // return bernoulli(ex_to_numeric(x))*pow(Pi,x)*numTWO().power(ex_to_numeric(x))/factorial(x);
53 throw (std::domain_error("you found a missing feature"));
55 if (x.info(info_flags::odd))
56 // return -bernoulli(1-ex_to_numeric(x))/(1-ex_to_numeric(x))
57 throw (std::domain_error("you found a missing feature"));
63 return zeta(x).hold();
66 static ex zeta_evalf(ex const & x)
70 END_TYPECHECK(zeta(x))
72 return zeta(ex_to_numeric(x));
75 static ex zeta_diff(ex const & x, unsigned diff_param)
77 ASSERT(diff_param==0);
79 return exZERO(); // should return zeta(numONE(),x);
82 static ex zeta_series(ex const & x, symbol const & s, ex const & point, int order)
84 throw(std::logic_error("don't know the series expansion of the zeta function"));
87 REGISTER_FUNCTION(zeta, zeta_eval, zeta_evalf, zeta_diff, zeta_series);