9cd0961af432694e0aed9a1c40ab26a50ead2918
[ginac.git] / ginac / inifcns_zeta.cpp
1 /** @file inifcns_zeta.cpp
2  *
3  *  Implementation of the Zeta-function and some related stuff. */
4
5 /*
6  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
7  *
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.
12  *
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.
17  *
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
21  */
22
23 #include <vector>
24 #include <stdexcept>
25
26 #include "inifcns.h"
27 #include "constant.h"
28 #include "numeric.h"
29 #include "power.h"
30 #include "symbol.h"
31 #include "utils.h"
32
33 namespace GiNaC {
34
35 //////////
36 // Riemann's Zeta-function
37 //////////
38
39 static ex zeta1_evalf(const ex & x)
40 {
41         BEGIN_TYPECHECK
42                 TYPECHECK(x,numeric)
43         END_TYPECHECK(zeta(x))
44                 
45         return zeta(ex_to<numeric>(x));
46 }
47
48 static ex zeta1_eval(const ex & x)
49 {
50         if (x.info(info_flags::numeric)) {
51                 numeric y = ex_to<numeric>(x);
52                 // trap integer arguments:
53                 if (y.is_integer()) {
54                         if (y.is_zero())
55                                 return -_ex1_2();
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();
61                                 else
62                                         return abs(bernoulli(y))*pow(Pi,x)*pow(_num2(),y-_num1())/factorial(y);
63                         } else {
64                                 if (x.info(info_flags::odd))
65                                         return -bernoulli(_num1()-y)/(_num1()-y);
66                                 else
67                                         return _num0();
68                         }
69                 }
70         }
71         return zeta(x).hold();
72 }
73
74 static ex zeta1_deriv(const ex & x, unsigned deriv_param)
75 {
76         GINAC_ASSERT(deriv_param==0);
77         
78         return zeta(_ex1(), x);
79 }
80
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).
86                                latex_name("\\zeta").
87                                overloaded(2));
88
89 //////////
90 // Derivatives of Riemann's Zeta-function  zeta(0,x)==zeta(x)
91 //////////
92
93 static ex zeta2_eval(const ex & n, const ex & x)
94 {
95         if (n.info(info_flags::numeric)) {
96                 // zeta(0,x) -> zeta(x)
97                 if (n.is_zero())
98                         return zeta(x);
99         }
100         
101         return zeta(n, x).hold();
102 }
103
104 static ex zeta2_deriv(const ex & n, const ex & x, unsigned deriv_param)
105 {
106         GINAC_ASSERT(deriv_param<2);
107         
108         if (deriv_param==0) {
109                 // d/dn zeta(n,x)
110                 throw(std::logic_error("cannot diff zeta(n,x) with respect to n"));
111         }
112         // d/dx psi(n,x)
113         return zeta(n+1,x);
114 }
115
116 const unsigned function_index_zeta2 =
117         function::register_new(function_options("zeta").
118                                eval_func(zeta2_eval).
119                                derivative_func(zeta2_deriv).
120                                latex_name("\\zeta").
121                                overloaded(2));
122
123 } // namespace GiNaC