This paper deals with the computation of the Lerch transcendent by means of the GaussLaguerre 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.

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

Denich E.
;
Novati P.
2023-01-01

Abstract

This paper deals with the computation of the Lerch transcendent by means of the GaussLaguerre 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.
2023
14-ago-2023
Epub ahead of print
https://link.springer.com/article/10.1007/s11075-023-01637-3
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/3055779
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