/** @file inifcns_zeta.cpp
 *
 *  Implementation of the Zeta-function and some related stuff. */

/*
 *  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
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

#include <vector>
#include <stdexcept>

#include "inifcns.h"
#include "constant.h"
#include "numeric.h"
#include "power.h"
#include "symbol.h"
#include "operators.h"
#include "utils.h"

namespace GiNaC {

//////////
// Derivatives of Riemann's Zeta-function  zeta(0,x)==zeta(x)
//////////

static ex zeta2_eval(const ex & n, const ex & x)
{
	if (n.info(info_flags::numeric)) {
		// zeta(0,x) -> zeta(x)
		if (n.is_zero())
			return zeta(x);
	}
	
	return zeta(n, x).hold();
}

static ex zeta2_deriv(const ex & n, const ex & x, unsigned deriv_param)
{
	GINAC_ASSERT(deriv_param<2);
	
	if (deriv_param==0) {
		// d/dn zeta(n,x)
		throw(std::logic_error("cannot diff zeta(n,x) with respect to n"));
	}
	// d/dx psi(n,x)
	return zeta(n+1,x);
}

unsigned zeta2_SERIAL::serial =
	function::register_new(function_options("zeta").
	                       eval_func(zeta2_eval).
	                       derivative_func(zeta2_deriv).
	                       latex_name("\\zeta").
	                       overloaded(2));

} // namespace GiNaC