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

DOI10.1007/s11075-023-01637-3arXiv2302.12065OpenAlexW4385808497MaRDI QIDQ6126588

Eleonora Denich, Paolo Novati

Publication date: 9 April 2024

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2302.12065

zbMATH Keywords

Lerch transcendentGauss-Laguerre rule

Mathematics Subject Classification ID

Numerical quadrature and cubature formulas (65D32) Hurwitz and Lerch zeta functions (11M35)

Cites Work

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• Crandall's computation of the incomplete gamma function and the Hurwitz zeta function, with applications to Dirichlet \(L\)-series
• Fast, reliable and unrestricted iterative computation of Gauss-Hermite and Gauss-Laguerre quadratures
• Discovery of the double exponential transformation and its developments
• Convergence Properties of Gaussian Quadrature Formulae
• Construction and implementation of asymptotic expansions for Laguerre-type orthogonal polynomials
• The Lerch function and the thermodynamical functions of the ideal quantum gases
• Calculation of Gauss Quadrature Rules
• Lagrange interpolation at Laguerre zeros in some weighted uniform spaces
• High-order asymptotic expansions of Gaussian quadrature rules with classical and generalized weight functions

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