A fast and simple algorithm for the computation of the Lerch transcendent
Numerical Analysis
2023-02-24 v1 Numerical Analysis
Abstract
This paper deals with the computation of the Lerch transcendent by means of the Gauss-Laguerre formula. An a priori estimate of the quadrature error, that allows to compute the number of quadrature nodes necessary to achieve an arbitrary precision, is derived. Exploiting the properties of the Gauss-Laguerre rule and the error estimate, a truncated approach is also considered. The algorithm used and its Matlab implementation are reported. The numerical examples confirm the reliability of this approach.
Keywords
Cite
@article{arxiv.2302.12065,
title = {A fast and simple algorithm for the computation of the Lerch transcendent},
author = {Eleonora Denich and Paolo Novati},
journal= {arXiv preprint arXiv:2302.12065},
year = {2023}
}