Abdelrahman Said
89 lines
2.8 KiB
C
89 lines
2.8 KiB
C
/* This file was imported from a private scientific library
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* based on GSL coined Home Scientific Libray (HSL) by its author
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* Jerome Benoit; this very material is itself inspired from the
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* material written by G. Jungan and distributed by GSL.
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* Ultimately, some modifications were done in order to render the
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* imported material independent from the rest of GSL.
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*/
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/* `hsl/hsl_sf_zeta.h' C header file
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// HSL - Home Scientific Library
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// Copyright (C) 2005-2018 Jerome Benoit
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//
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// HSL is free software; you can redistribute it and/or
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// modify it under the terms of the GNU General Public License
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// as published by the Free Software Foundation; either version 2
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// of the License, or (at your option) any later version.
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//
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// This program is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU General Public License
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// along with this program; if not, write to the Free Software
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// Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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*/
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/* For futher details, see its source conterpart src/hzeta.c */
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/* Author: Jerome G. Benoit < jgmbenoit _at_ rezozer _dot_ net > */
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#ifndef __HZETA_H__
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#define __HZETA_H__
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#include "plfit_decls.h"
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PLFIT_BEGIN_C_DECLS
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/* Hurwitz Zeta Function
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* zeta(s,q) = Sum[ (k+q)^(-s), {k,0,Infinity} ]
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*
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* s > 1.0, q > 0.0
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*/
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double hsl_sf_hzeta(const double s, const double q);
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/* First Derivative of Hurwitz Zeta Function
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* zeta'(s,q) = - Sum[ Ln(k+q)/(k+q)^(s), {k,0,Infinity} ]
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*
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* s > 1.0, q > 0.0
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*/
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double hsl_sf_hzeta_deriv(const double s, const double q);
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/* Second Derivative of Hurwitz Zeta Function
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* zeta''(s,q) = + Sum[ Ln(k+q)^2/(k+q)^(s), {k,0,Infinity} ]
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*
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* s > 1.0, q > 0.0
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*/
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double hsl_sf_hzeta_deriv2(const double s, const double q);
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/* Logarithm of Hurwitz Zeta Function
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* lnzeta(s,q) = ln(zeta(s,q))
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*
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* s > 1.0, q > 0.0 (and q >> 1)
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*/
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double hsl_sf_lnhzeta(const double s, const double q);
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/* Logarithmic Derivative of Hurwitz Zeta Function
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* lnzeta'(s,q) = zeta'(s,q)/zeta(s,q)
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*
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* s > 1.0, q > 0.0 (and q >> 1)
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*/
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double hsl_sf_lnhzeta_deriv(const double s, const double q);
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/* Logarithm and Logarithmic Derivative of Hurwitz Zeta Function:
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* nonredundant computation version:
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* - lnzeta(s,q) and lnzeta'(s,q) are stored in *deriv0 and *deriv1, respectively;
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* - the return value and the value stored in *deriv0 are the same;
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* - deriv0 and deriv1 must be effective pointers, that is, not the NULL pointer.
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*
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* s > 1.0, q > 0.0 (and q >> 1)
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*/
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double hsl_sf_lnhzeta_deriv_tuple(const double s, const double q, double * deriv0, double * deriv1);
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PLFIT_END_C_DECLS
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#endif // __HZETA_H__
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