1 /** @file inifcns_zeta.cpp
3 * Implementation of the Zeta-function and some related stuff. */
6 * GiNaC Copyright (C) 1999-2001 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
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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.
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20 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
36 // Riemann's Zeta-function
39 static ex zeta1_evalf(const ex & x)
43 END_TYPECHECK(zeta(x))
45 return zeta(ex_to_numeric(x));
48 static ex zeta1_eval(const ex & x)
50 if (x.info(info_flags::numeric)) {
51 numeric y = ex_to_numeric(x);
52 // trap integer arguments:
56 if (x.is_equal(_ex1()))
57 throw(std::domain_error("zeta(1): infinity"));
58 if (x.info(info_flags::posint)) {
59 if (x.info(info_flags::odd))
60 return zeta(x).hold();
62 return abs(bernoulli(y))*pow(Pi,x)*pow(_num2(),y-_num1())/factorial(y);
64 if (x.info(info_flags::odd))
65 return -bernoulli(_num1()-y)/(_num1()-y);
71 return zeta(x).hold();
74 static ex zeta1_deriv(const ex & x, unsigned deriv_param)
76 GINAC_ASSERT(deriv_param==0);
78 return zeta(_ex1(), x);
81 const unsigned function_index_zeta1 =
82 function::register_new(function_options("zeta").
83 eval_func(zeta1_eval).
84 evalf_func(zeta1_evalf).
85 derivative_func(zeta1_deriv).
90 // Derivatives of Riemann's Zeta-function zeta(0,x)==zeta(x)
93 static ex zeta2_eval(const ex & n, const ex & x)
95 if (n.info(info_flags::numeric)) {
96 // zeta(0,x) -> zeta(x)
101 return zeta(n, x).hold();
104 static ex zeta2_deriv(const ex & n, const ex & x, unsigned deriv_param)
106 GINAC_ASSERT(deriv_param<2);
108 if (deriv_param==0) {
110 throw(std::logic_error("cannot diff zeta(n,x) with respect to n"));
116 const unsigned function_index_zeta2 =
117 function::register_new(function_options("zeta").
118 eval_func(zeta2_eval).
119 derivative_func(zeta2_deriv).