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) 1999-2000 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 "ex.h"
  28 #include "constant.h"
  29 #include "numeric.h"
  30 #include "power.h"
  31 #include "symbol.h"
  32 #include "utils.h"
  33
  34 #ifndef NO_NAMESPACE_GINAC
  35 namespace GiNaC {
  36 #endif // ndef NO_NAMESPACE_GINAC
  37
  38 //////////
  39 // Riemann's Zeta-function
  40 //////////
  41
  42 static ex zeta1_evalf(const ex & x)
  43 {
  44         BEGIN_TYPECHECK
  45                 TYPECHECK(x,numeric)
  46         END_TYPECHECK(zeta(x))
  47
  48         return zeta(ex_to_numeric(x));
  49 }
  50
  51 static ex zeta1_eval(const ex & x)
  52 {
  53         if (x.info(info_flags::numeric)) {
  54                 numeric y = ex_to_numeric(x);
  55                 // trap integer arguments:
  56                 if (y.is_integer()) {
  57                         if (y.is_zero())
  58                                 return -_ex1_2();
  59                         if (x.is_equal(_ex1()))
  60                                 throw(std::domain_error("zeta(1): infinity"));
  61                         if (x.info(info_flags::posint)) {
  62                                 if (x.info(info_flags::odd))
  63                                         return zeta(x).hold();
  64                                 else
  65                                         return abs(bernoulli(y))*pow(Pi,x)*pow(_num2(),y-_num1())/factorial(y);
  66                         } else {
  67                                 if (x.info(info_flags::odd))
  68                                         return -bernoulli(_num1()-y)/(_num1()-y);
  69                                 else
  70                                         return _num0();
  71                         }
  72                 }
  73         }
  74         return zeta(x).hold();
  75 }
  76
  77 static ex zeta1_deriv(const ex & x, unsigned deriv_param)
  78 {
  79         GINAC_ASSERT(deriv_param==0);
  80
  81         return zeta(_ex1(), x);
  82 }
  83
  84 const unsigned function_index_zeta1 =
  85         function::register_new(function_options("zeta").
  86                                eval_func(zeta1_eval).
  87                                evalf_func(zeta1_evalf).
  88                                derivative_func(zeta1_deriv).
  89                                overloaded(2));
  90
  91 //////////
  92 // Derivatives of Riemann's Zeta-function  zeta(0,x)==zeta(x)
  93 //////////
  94
  95 static ex zeta2_eval(const ex & n, const ex & x)
  96 {
  97         if (n.info(info_flags::numeric)) {
  98                 // zeta(0,x) -> zeta(x)
  99                 if (n.is_zero())
 100                         return zeta(x);
 101         }
 102
 103         return zeta(n, x).hold();
 104 }
 105
 106 static ex zeta2_deriv(const ex & n, const ex & x, unsigned deriv_param)
 107 {
 108         GINAC_ASSERT(deriv_param<2);
 109
 110         if (deriv_param==0) {
 111                 // d/dn zeta(n,x)
 112                 throw(std::logic_error("cannot diff zeta(n,x) with respect to n"));
 113         }
 114         // d/dx psi(n,x)
 115         return zeta(n+1,x);
 116 }
 117
 118 const unsigned function_index_zeta2 =
 119         function::register_new(function_options("zeta").
 120                                eval_func(zeta2_eval).
 121                                derivative_func(zeta2_deriv).
 122                                overloaded(2));
 123
 124 #ifndef NO_NAMESPACE_GINAC
 125 } // namespace GiNaC
 126 #endif // ndef NO_NAMESPACE_GINAC