English

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}
}
R2 v1 2026-06-28T08:47:57.731Z