epsteinZeta.c File Reference

Calculates the (regularized) Epstein zeta function. More...

#include <complex.h>
#include <stdbool.h>
#include "epsteinZeta.h"
#include "zeta.h"

Include dependency graph for epsteinZeta.c:

Functions
double complex	epsteinZeta (double nu, unsigned int dim, const double *a, const double *x, const double *y)
	calculates the Epstein Zeta function.
double complex	epsteinZetaReg (double nu, unsigned int dim, const double *a, const double *x, const double *y)
	calculates the regularized Epstein Zeta function.

Detailed Description

Calculates the (regularized) Epstein zeta function.

Author

Andreas Buchheit, Jonathan Busse and Ruben Gutendorf.

See also

Crandall, R., Unified algorithms for polylogarithm, L-series, and zeta variants. Algorithmic Reflections: Selected Works. PSIpress (2012).

Author

Andreas Buchheit, Jonathan Busse and Ruben Gutendorf.

Date

06/13/2024

Function Documentation

epsteinZeta()

double complex epsteinZeta	(	double	nu,
		unsigned int	dim,
		const double *	a,
		const double *	x,
		const double *	y )

calculates the Epstein Zeta function.

Parameters

[in]	nu	exponent for the Epstein zeta function.
[in]	dim	dimension of the input vectors.
[in]	a	matrix that transforms the lattice in the Epstein Zeta function.
[in]	x	x vector of the Epstein Zeta function.
[in]	y	y vector of the Epstein Zeta function.

Returns

function value of the Epstein zeta.

epsteinZetaReg()

double complex epsteinZetaReg	(	double	nu,
		unsigned int	dim,
		const double *	a,
		const double *	x,
		const double *	y )

calculates the regularized Epstein Zeta function.

Parameters

[in]	nu	exponent for the Epstein zeta function.
[in]	dim	dimension of the input vectors.
[in]	a	matrix that transforms the lattice in the Epstein Zeta function.
[in]	x	x vector of the Epstein Zeta function.
[in]	y	y vector of the Epstein Zeta function.

Returns

function value of the regularized Epstein zeta.