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 #ifndef NO_NAMESPACE_GINAC
  34 namespace GiNaC {
  35 #endif // ndef NO_NAMESPACE_GINAC
  36
  37 //////////
  38 // Riemann's Zeta-function
  39 //////////
  40
  41 static ex zeta1_evalf(const ex & x)
  42 {
  43         BEGIN_TYPECHECK
  44                 TYPECHECK(x,numeric)
  45         END_TYPECHECK(zeta(x))
  46
  47         return zeta(ex_to_numeric(x));
  48 }
  49
  50 static ex zeta1_eval(const ex & x)
  51 {
  52         if (x.info(info_flags::numeric)) {
  53                 numeric y = ex_to_numeric(x);
  54                 // trap integer arguments:
  55                 if (y.is_integer()) {
  56                         if (y.is_zero())
  57                                 return -_ex1_2();
  58                         if (x.is_equal(_ex1()))
  59                                 throw(std::domain_error("zeta(1): infinity"));
  60                         if (x.info(info_flags::posint)) {
  61                                 if (x.info(info_flags::odd))
  62                                         return zeta(x).hold();
  63                                 else
  64                                         return abs(bernoulli(y))*pow(Pi,x)*pow(_num2(),y-_num1())/factorial(y);
  65                         } else {
  66                                 if (x.info(info_flags::odd))
  67                                         return -bernoulli(_num1()-y)/(_num1()-y);
  68                                 else
  69                                         return _num0();
  70                         }
  71                 }
  72         }
  73         return zeta(x).hold();
  74 }
  75
  76 static ex zeta1_deriv(const ex & x, unsigned deriv_param)
  77 {
  78         GINAC_ASSERT(deriv_param==0);
  79
  80         return zeta(_ex1(), x);
  81 }
  82
  83 const unsigned function_index_zeta1 =
  84         function::register_new(function_options("zeta").
  85                                eval_func(zeta1_eval).
  86                                evalf_func(zeta1_evalf).
  87                                derivative_func(zeta1_deriv).
  88                                overloaded(2));
  89
  90 //////////
  91 // Derivatives of Riemann's Zeta-function  zeta(0,x)==zeta(x)
  92 //////////
  93
  94 static ex zeta2_eval(const ex & n, const ex & x)
  95 {
  96         if (n.info(info_flags::numeric)) {
  97                 // zeta(0,x) -> zeta(x)
  98                 if (n.is_zero())
  99                         return zeta(x);
 100         }
 101
 102         return zeta(n, x).hold();
 103 }
 104
 105 static ex zeta2_deriv(const ex & n, const ex & x, unsigned deriv_param)
 106 {
 107         GINAC_ASSERT(deriv_param<2);
 108
 109         if (deriv_param==0) {
 110                 // d/dn zeta(n,x)
 111                 throw(std::logic_error("cannot diff zeta(n,x) with respect to n"));
 112         }
 113         // d/dx psi(n,x)
 114         return zeta(n+1,x);
 115 }
 116
 117 const unsigned function_index_zeta2 =
 118         function::register_new(function_options("zeta").
 119                                eval_func(zeta2_eval).
 120                                derivative_func(zeta2_deriv).
 121                                overloaded(2));
 122
 123 #ifndef NO_NAMESPACE_GINAC
 124 } // namespace GiNaC
 125 #endif // ndef NO_NAMESPACE_GINAC