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         if (is_exactly_a<numeric>(x)) {
  42                 try {
  43                         return zeta(ex_to<numeric>(x));
  44                 } catch (const dunno &e) { }
  45         }
  46
  47         return zeta(x).hold();
  48 }
  49
  50 static ex zeta1_eval(const ex & x)
  51 {
  52         if (x.info(info_flags::numeric)) {
  53                 const numeric &y = ex_to<numeric>(x);
  54                 // trap integer arguments:
  55                 if (y.is_integer()) {
  56                         if (y.is_zero())
  57                                 return _ex_1_2;
  58                         if (y.is_equal(_num1))
  59                                 throw(std::domain_error("zeta(1): infinity"));
  60                         if (y.info(info_flags::posint)) {
  61                                 if (y.info(info_flags::odd))
  62                                         return zeta(x).hold();
  63                                 else
  64                                         return abs(bernoulli(y))*pow(Pi,y)*pow(_num2,y-_num1)/factorial(y);
  65                         } else {
  66                                 if (y.info(info_flags::odd))
  67                                         return -bernoulli(_num1-y)/(_num1-y);
  68                                 else
  69                                         return _ex0;
  70                         }
  71                 }
  72                 // zeta(float)
  73                 if (y.info(info_flags::numeric) && !y.info(info_flags::crational))
  74                         return zeta1_evalf(x);
  75         }
  76         return zeta(x).hold();
  77 }
  78
  79 static ex zeta1_deriv(const ex & x, unsigned deriv_param)
  80 {
  81         GINAC_ASSERT(deriv_param==0);
  82
  83         return zeta(_ex1, x);
  84 }
  85
  86 const unsigned function_index_zeta1 =
  87         function::register_new(function_options("zeta").
  88                                eval_func(zeta1_eval).
  89                                evalf_func(zeta1_evalf).
  90                                derivative_func(zeta1_deriv).
  91                                latex_name("\\zeta").
  92                                overloaded(2));
  93
  94 //////////
  95 // Derivatives of Riemann's Zeta-function  zeta(0,x)==zeta(x)
  96 //////////
  97
  98 static ex zeta2_eval(const ex & n, const ex & x)
  99 {
 100         if (n.info(info_flags::numeric)) {
 101                 // zeta(0,x) -> zeta(x)
 102                 if (n.is_zero())
 103                         return zeta(x);
 104         }
 105
 106         return zeta(n, x).hold();
 107 }
 108
 109 static ex zeta2_deriv(const ex & n, const ex & x, unsigned deriv_param)
 110 {
 111         GINAC_ASSERT(deriv_param<2);
 112
 113         if (deriv_param==0) {
 114                 // d/dn zeta(n,x)
 115                 throw(std::logic_error("cannot diff zeta(n,x) with respect to n"));
 116         }
 117         // d/dx psi(n,x)
 118         return zeta(n+1,x);
 119 }
 120
 121 const unsigned function_index_zeta2 =
 122         function::register_new(function_options("zeta").
 123                                eval_func(zeta2_eval).
 124                                derivative_func(zeta2_deriv).
 125                                latex_name("\\zeta").
 126                                overloaded(2));
 127
 128 } // namespace GiNaC