Add graph references

2026-06-28 13:49:01 +01:00
parent 0a9807e448
commit a11edf0c53
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+/* This file was imported from a private scientific library
+ * based on GSL coined Home Scientific Libray (HSL) by its author
+ * Jerome Benoit; this very material is itself inspired from the
+ * material written by G. Jungan and distributed by GSL.
+ * Ultimately, some modifications were done in order to render the
+ * imported material independent from the rest of GSL.
+ */
+
+/* `hsl/hsl_sf_zeta.h' C header file
+// HSL - Home Scientific Library
+// Copyright (C) 2005-2018  Jerome Benoit
+//
+// HSL 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+*/
+
+/* For futher details, see its source conterpart src/hzeta.c */
+
+/* Author:  Jerome G. Benoit < jgmbenoit _at_ rezozer _dot_ net > */
+
+#ifndef __HZETA_H__
+#define __HZETA_H__
+
+#include "plfit_decls.h"
+
+PLFIT_BEGIN_C_DECLS
+
+
+/* Hurwitz Zeta Function
+ * zeta(s,q) = Sum[ (k+q)^(-s), {k,0,Infinity} ]
+ *
+ * s > 1.0, q > 0.0
+ */
+double hsl_sf_hzeta(const double s, const double q);
+
+/* First Derivative of Hurwitz Zeta Function
+ * zeta'(s,q) = - Sum[ Ln(k+q)/(k+q)^(s), {k,0,Infinity} ]
+ *
+ * s > 1.0, q > 0.0
+ */
+double hsl_sf_hzeta_deriv(const double s, const double q);
+
+/* Second Derivative of Hurwitz Zeta Function
+ * zeta''(s,q) = + Sum[ Ln(k+q)^2/(k+q)^(s), {k,0,Infinity} ]
+ *
+ * s > 1.0, q > 0.0
+ */
+double hsl_sf_hzeta_deriv2(const double s, const double q);
+
+/* Logarithm of Hurwitz Zeta Function
+ * lnzeta(s,q) = ln(zeta(s,q))
+ *
+ * s > 1.0, q > 0.0 (and q >> 1)
+ */
+double hsl_sf_lnhzeta(const double s, const double q);
+
+/* Logarithmic Derivative of Hurwitz Zeta Function
+ * lnzeta'(s,q) = zeta'(s,q)/zeta(s,q)
+ *
+ * s > 1.0, q > 0.0 (and q >> 1)
+ */
+double hsl_sf_lnhzeta_deriv(const double s, const double q);
+
+/* Logarithm and Logarithmic Derivative of Hurwitz Zeta Function:
+ * nonredundant computation version:
+ * - lnzeta(s,q) and lnzeta'(s,q) are stored in *deriv0 and *deriv1, respectively;
+ * - the return value and the value stored in *deriv0 are the same;
+ * - deriv0 and deriv1 must be effective pointers, that is, not the NULL pointer.
+ *
+ * s > 1.0, q > 0.0 (and q >> 1)
+ */
+double hsl_sf_lnhzeta_deriv_tuple(const double s, const double q, double * deriv0, double * deriv1);
+
+
+PLFIT_END_C_DECLS
+
+#endif // __HZETA_H__