orthopoly.h

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/*
 * Copyright (c) 2009-2015:  G-CSC, Goethe University Frankfurt
 * Author: Dmitry Logashenko
 * 
 * This file is part of UG4.
 * 
 * UG4 is free software: you can redistribute it and/or modify it under the
 * terms of the GNU Lesser General Public License version 3 (as published by the
 * Free Software Foundation) with the following additional attribution
 * requirements (according to LGPL/GPL v3 §7):
 * 
 * (1) The following notice must be displayed in the Appropriate Legal Notices
 * of covered and combined works: "Based on UG4 (www.ug4.org/license)".
 * 
 * (2) The following notice must be displayed at a prominent place in the
 * terminal output of covered works: "Based on UG4 (www.ug4.org/license)".
 * 
 * (3) The following bibliography is recommended for citation and must be
 * preserved in all covered files:
 * "Reiter, S., Vogel, A., Heppner, I., Rupp, M., and Wittum, G. A massively
 *   parallel geometric multigrid solver on hierarchically distributed grids.
 *   Computing and visualization in science 16, 4 (2013), 151-164"
 * "Vogel, A., Reiter, S., Rupp, M., Nägel, A., and Wittum, G. UG4 -- a novel
 *   flexible software system for simulating pde based models on high performance
 *   computers. Computing and visualization in science 16, 4 (2013), 165-179"
 * 
 * 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 Lesser General Public License for more details.
 */
 
#ifndef __H__UGMATH__ORTHO_POLY__
#define __H__UGMATH__ORTHO_POLY__
 
#include "common/types.h"
 
namespace ug
{
 
// computes the Legendre polynomials
number LegendrePoly (size_t k, number x);
 
// computes the scalar square of the Legendre polynomials
number SqNormOfLegendrePoly (size_t k);
 
// computes the normalized Legendre polynomials
number NormalizedLegendrePoly (size_t k, number x);
 
// computes the Chebyshev polynomials of the first kind
number Chebyshev1Poly (size_t k, number x);
 
// computes the scalar square of the Chebyshev polynomials of the first kind
number SqNormOfChebyshev1Poly (size_t k);
 
// computes the normalized Chebyshev polynomials of the first kind
number NormalizedChebyshev1Poly (size_t k, number x);
 
// computes the Chebyshev polynomials of the second kind
number Chebyshev2Poly (size_t k, number x);
 
// computes the scalar square of the Chebyshev polynomials of the second kind
number SqNormOfChebyshev2Poly (size_t k);
 
// computes the normalized Chebyshev polynomials of the second kind
number NormalizedChebyshev2Poly (size_t k, number x);
 
} // namespace ug
 
#endif // __H__UGMATH__ORTHO_POLY__
 
/* End of File */