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) 1999-2003 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 "operators.h"
  32 #include "utils.h"
  33
  34 namespace GiNaC {
  35
  36 //////////
  37 // Riemann's Zeta-function
  38 //////////
  39
  40 static ex zeta1_evalf(const ex & x)
  41 {
  42         if (is_exactly_a<numeric>(x)) {
  43                 try {
  44                         return zeta(ex_to<numeric>(x));
  45                 } catch (const dunno &e) { }
  46         }
  47
  48         return zeta(x).hold();
  49 }
  50
  51 static ex zeta1_eval(const ex & x)
  52 {
  53         if (x.info(info_flags::numeric)) {
  54                 const numeric &y = ex_to<numeric>(x);
  55                 // trap integer arguments:
  56                 if (y.is_integer()) {
  57                         if (y.is_zero())
  58                                 return _ex_1_2;
  59                         if (y.is_equal(_num1))
  60                                 throw(std::domain_error("zeta(1): infinity"));
  61                         if (y.info(info_flags::posint)) {
  62                                 if (y.info(info_flags::odd))
  63                                         return zeta(x).hold();
  64                                 else
  65                                         return abs(bernoulli(y))*pow(Pi,y)*pow(_num2,y-_num1)/factorial(y);
  66                         } else {
  67                                 if (y.info(info_flags::odd))
  68                                         return -bernoulli(_num1-y)/(_num1-y);
  69                                 else
  70                                         return _ex0;
  71                         }
  72                 }
  73                 // zeta(float)
  74                 if (y.info(info_flags::numeric) && !y.info(info_flags::crational))
  75                         return zeta1_evalf(x);
  76         }
  77         return zeta(x).hold();
  78 }
  79
  80 static ex zeta1_deriv(const ex & x, unsigned deriv_param)
  81 {
  82         GINAC_ASSERT(deriv_param==0);
  83
  84         return zeta(_ex1, x);
  85 }
  86
  87 unsigned zeta1_SERIAL::serial =
  88         function::register_new(function_options("zeta").
  89                                eval_func(zeta1_eval).
  90                                evalf_func(zeta1_evalf).
  91                                derivative_func(zeta1_deriv).
  92                                latex_name("\\zeta").
  93                                overloaded(2));
  94
  95 //////////
  96 // Derivatives of Riemann's Zeta-function  zeta(0,x)==zeta(x)
  97 //////////
  98
  99 static ex zeta2_eval(const ex & n, const ex & x)
 100 {
 101         if (n.info(info_flags::numeric)) {
 102                 // zeta(0,x) -> zeta(x)
 103                 if (n.is_zero())
 104                         return zeta(x);
 105         }
 106
 107         return zeta(n, x).hold();
 108 }
 109
 110 static ex zeta2_deriv(const ex & n, const ex & x, unsigned deriv_param)
 111 {
 112         GINAC_ASSERT(deriv_param<2);
 113
 114         if (deriv_param==0) {
 115                 // d/dn zeta(n,x)
 116                 throw(std::logic_error("cannot diff zeta(n,x) with respect to n"));
 117         }
 118         // d/dx psi(n,x)
 119         return zeta(n+1,x);
 120 }
 121
 122 unsigned zeta2_SERIAL::serial =
 123         function::register_new(function_options("zeta").
 124                                eval_func(zeta2_eval).
 125                                derivative_func(zeta2_deriv).
 126                                latex_name("\\zeta").
 127                                overloaded(2));
 128
 129 } // namespace GiNaC