* Implementation of the Zeta-function and some related stuff. */
/*
- * GiNaC Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
#include "numeric.h"
#include "power.h"
#include "symbol.h"
+#include "operators.h"
#include "utils.h"
namespace GiNaC {
-//////////
-// Riemann's Zeta-function
-//////////
-
-static ex zeta1_evalf(const ex & x)
-{
- if (is_exactly_a<numeric>(x)) {
- try {
- return zeta(ex_to<numeric>(x));
- } catch (const dunno &e) { }
- }
-
- return zeta(x).hold();
-}
-
-static ex zeta1_eval(const ex & x)
-{
- if (x.info(info_flags::numeric)) {
- const numeric &y = ex_to<numeric>(x);
- // trap integer arguments:
- if (y.is_integer()) {
- if (y.is_zero())
- return _ex_1_2;
- if (y.is_equal(_num1))
- throw(std::domain_error("zeta(1): infinity"));
- if (y.info(info_flags::posint)) {
- if (y.info(info_flags::odd))
- return zeta(x).hold();
- else
- return abs(bernoulli(y))*pow(Pi,y)*pow(_num2,y-_num1)/factorial(y);
- } else {
- if (y.info(info_flags::odd))
- return -bernoulli(_num1-y)/(_num1-y);
- else
- return _ex0;
- }
- }
- // zeta(float)
- if (y.info(info_flags::numeric) && !y.info(info_flags::crational))
- return zeta1_evalf(x);
- }
- return zeta(x).hold();
-}
-
-static ex zeta1_deriv(const ex & x, unsigned deriv_param)
-{
- GINAC_ASSERT(deriv_param==0);
-
- return zeta(_ex1, x);
-}
-
-const unsigned function_index_zeta1 =
- function::register_new(function_options("zeta").
- eval_func(zeta1_eval).
- evalf_func(zeta1_evalf).
- derivative_func(zeta1_deriv).
- latex_name("\\zeta").
- overloaded(2));
-
//////////
// Derivatives of Riemann's Zeta-function zeta(0,x)==zeta(x)
//////////
return zeta(n+1,x);
}
-const unsigned function_index_zeta2 =
+unsigned zeta2_SERIAL::serial =
function::register_new(function_options("zeta").
eval_func(zeta2_eval).
derivative_func(zeta2_deriv).