Epstein Zeta Library 0.6.2
Calculates the Epstein Zeta function
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crandall.h
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1// SPDX-FileCopyrightText: 2024 Andreas Buchheit <buchheit@num.uni-sb.de>
2// SPDX-FileCopyrightText: 2024 Jonathan Busse <jonathan@jbusse.de>
3// SPDX-FileCopyrightText: 2024 Ruben Gutendorf
4// <ruben.gutendorf@uni-saarland.de>
5//
6// SPDX-License-Identifier: AGPL-3.0-only
7
14#include <complex.h>
15
16#ifndef EPSTEIN_CRANDALL
17#define EPSTEIN_CRANDALL
18
26double assignzArgBound(double nu);
27
41double complex crandall_g(unsigned int dim, double nu, const double *z,
42 double prefactor, double zArgBound);
43
55double complex crandall_gReg_nuequalsdim(double s, double arg, double k,
56 double lambda);
57
72double complex crandall_gReg(unsigned int dim, double s, const double *z,
73 double prefactor);
74
90double crandall_gReg_harmonic(int k, int n, unsigned int dim, double s,
91 const double *z, double prefactor);
92
103double complex crandall_g_lower(unsigned int dim, double nu, const double *z,
104 double prefactor);
105
106double polynomial_y_der(unsigned int k, unsigned int dim, const double *z,
107 const unsigned int *alpha, unsigned int alphaAbs,
108 unsigned int n);
109
121double complex crandall_gReg_nuequalsdimplus2k(double s, double arg, double k,
122 double lambda);
123
124#endif
double complex crandall_gReg(unsigned int dim, double s, const double *z, double prefactor)
Calculates the regularization of the zero summand in the second sum in Crandall's formula.
Definition crandall.c:139
double complex crandall_g(unsigned int dim, double nu, const double *z, double prefactor, double zArgBound)
Calculates the upper Crandall function.
Definition crandall.c:68
double assignzArgBound(double nu)
calculates bounds on when to use asymptotic expansion of the upper incomplete gamma function,...
Definition crandall.c:40
double complex crandall_gReg_nuequalsdim(double s, double arg, double k, double lambda)
Calculates the regularization of the zero summand in the second sum in Crandall's formula in the spec...
double polynomial_y_der(unsigned int k, unsigned int dim, const double *z, const unsigned int *alpha, unsigned int alphaAbs, unsigned int n)
Calculates the derivatives of Y_k(z) / n! = (pi * z**2)**k / n! where n <= k.
Definition crandall.c:302
double complex crandall_gReg_nuequalsdimplus2k(double s, double arg, double k, double lambda)
Calculates the regularization of the zero summand in the second sum in Crandall's formula in the spec...
Definition crandall.c:94
double complex crandall_g_lower(unsigned int dim, double nu, const double *z, double prefactor)
Calculates the lower Crandall function.
Definition crandall.c:248
double crandall_gReg_harmonic(int k, int n, unsigned int dim, double s, const double *z, double prefactor)
Calculates the regularization of the zero summand in the second sum in Crandall's formula for the har...
Definition crandall.c:275