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Diffstat (limited to 'thirdparty/includes/GSL/gsl/gsl_sf_dilog.h')
-rw-r--r-- | thirdparty/includes/GSL/gsl/gsl_sf_dilog.h | 130 |
1 files changed, 0 insertions, 130 deletions
diff --git a/thirdparty/includes/GSL/gsl/gsl_sf_dilog.h b/thirdparty/includes/GSL/gsl/gsl_sf_dilog.h deleted file mode 100644 index 79b2b76f..00000000 --- a/thirdparty/includes/GSL/gsl/gsl_sf_dilog.h +++ /dev/null @@ -1,130 +0,0 @@ -/* specfunc/gsl_sf_dilog.h - * - * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004 Gerard Jungman - * - * 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 3 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. - */ - -/* Author: G. Jungman */ - -#ifndef __GSL_SF_DILOG_H__ -#define __GSL_SF_DILOG_H__ - -#include <gsl/gsl_sf_result.h> - -#undef __BEGIN_DECLS -#undef __END_DECLS -#ifdef __cplusplus -# define __BEGIN_DECLS extern "C" { -# define __END_DECLS } -#else -# define __BEGIN_DECLS /* empty */ -# define __END_DECLS /* empty */ -#endif - -__BEGIN_DECLS - - -/* Real part of DiLogarithm(x), for real argument. - * In Lewin's notation, this is Li_2(x). - * - * Li_2(x) = - Re[ Integrate[ Log[1-s] / s, {s, 0, x}] ] - * - * The function in the complex plane has a branch point - * at z = 1; we place the cut in the conventional way, - * on [1, +infty). This means that the value for real x > 1 - * is a matter of definition; however, this choice does not - * affect the real part and so is not relevant to the - * interpretation of this implemented function. - */ -int gsl_sf_dilog_e(const double x, gsl_sf_result * result); -double gsl_sf_dilog(const double x); - - -/* DiLogarithm(z), for complex argument z = x + i y. - * Computes the principal branch. - * - * Recall that the branch cut is on the real axis with x > 1. - * The imaginary part of the computed value on the cut is given - * by -Pi*log(x), which is the limiting value taken approaching - * from y < 0. This is a conventional choice, though there is no - * true standardized choice. - * - * Note that there is no canonical way to lift the defining - * contour to the full Riemann surface because of the appearance - * of a "hidden branch point" at z = 0 on non-principal sheets. - * Experts will know the simple algebraic prescription for - * obtaining the sheet they want; non-experts will not want - * to know anything about it. This is why GSL chooses to compute - * only on the principal branch. - */ -int -gsl_sf_complex_dilog_xy_e( - const double x, - const double y, - gsl_sf_result * result_re, - gsl_sf_result * result_im - ); - - - -/* DiLogarithm(z), for complex argument z = r Exp[i theta]. - * Computes the principal branch, thereby assuming an - * implicit reduction of theta to the range (-2 pi, 2 pi). - * - * If theta is identically zero, the imaginary part is computed - * as if approaching from y > 0. For other values of theta no - * special consideration is given, since it is assumed that - * no other machine representations of multiples of pi will - * produce y = 0 precisely. This assumption depends on some - * subtle properties of the machine arithmetic, such as - * correct rounding and monotonicity of the underlying - * implementation of sin() and cos(). - * - * This function is ok, but the interface is confusing since - * it makes it appear that the branch structure is resolved. - * Furthermore the handling of values close to the branch - * cut is subtle. Perhap this interface should be deprecated. - */ -int -gsl_sf_complex_dilog_e( - const double r, - const double theta, - gsl_sf_result * result_re, - gsl_sf_result * result_im - ); - - - -/* Spence integral; spence(s) := Li_2(1-s) - * - * This function has a branch point at 0; we place the - * cut on (-infty,0). Because of our choice for the value - * of Li_2(z) on the cut, spence(s) is continuous as - * s approaches the cut from above. In other words, - * we define spence(x) = spence(x + i 0+). - */ -int -gsl_sf_complex_spence_xy_e( - const double x, - const double y, - gsl_sf_result * real_sp, - gsl_sf_result * imag_sp - ); - - -__END_DECLS - -#endif /* __GSL_SF_DILOG_H__ */ |