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                                overloaded(2));
  87
  88 //////////
  89 // Derivatives of Riemann's Zeta-function  zeta(0,x)==zeta(x)
  90 //////////
  91
  92 static ex zeta2_eval(const ex & n, const ex & x)
  93 {
  94         if (n.info(info_flags::numeric)) {
  95                 // zeta(0,x) -> zeta(x)
  96                 if (n.is_zero())
  97                         return zeta(x);
  98         }
  99
 100         return zeta(n, x).hold();
 101 }
 102
 103 static ex zeta2_deriv(const ex & n, const ex & x, unsigned deriv_param)
 104 {
 105         GINAC_ASSERT(deriv_param<2);
 106
 107         if (deriv_param==0) {
 108                 // d/dn zeta(n,x)
 109                 throw(std::logic_error("cannot diff zeta(n,x) with respect to n"));
 110         }
 111         // d/dx psi(n,x)
 112         return zeta(n+1,x);
 113 }
 114
 115 const unsigned function_index_zeta2 =
 116         function::register_new(function_options("zeta").
 117                                eval_func(zeta2_eval).
 118                                derivative_func(zeta2_deriv).
 119                                overloaded(2));
 120
 121 } // namespace GiNaC