Work

High-precision numerical evaluation of Lauricella functions

Year: 2025

Type: article

Abstract: We present a method for high-precision numerical evaluations of Lauricella functions whose indices are linearly dependent on some parameter ε in terms of their Laurent series expansions at zero. This method is based on finding analytic continuations of these functions in terms of Frobenius generalized power series. Being one-dimensional, these series are much more suited for high-precision numerical evaluations than multi-dimensional sums arising in approaches to analytic continuations based on re-expansions of hypergeometric series or Mellin–Barnes integral representations. To accelerate the calculation procedure further, the ε dependence of the result is reconstructed from the evaluations of given Lauricella functions at specific numerical values of ε , which, in addition, allows for efficient parallel implementation. The method has been implemented in the PrecisionLauricella package, written in Wolfram Mathematica language.

Source: Nuclear Physics B

DOI: 10.1016/j.nuclphysb.2025.116994

Authors: M.A. Bezuglov, B.A. Kniehl, A.I. Onishchenko, O.L. Veretin

Institutions: Universität Hamburg, Joint Institute for Nuclear Research, Budker Institute of Nuclear Physics, University of Regensburg

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Deutsche Forschungsgemeinschaft, Russian Science Foundation

Awards: G3164835508, G5594808391, G6808547609