A fast and simple algorithm for the computation of the Lerch transcendent

• DOI: 10.1007/s11075-023-01637-3
• Publication Date: 2023-08-14T05:02:01Z
• Authors: Eleonora Denich; Paolo Novati
• Keywords: Theory of computation; Quadrature (astronomy); Laguerre polynomials

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.