Bezuglov, M. A. and Kniehl, B. A. and Onishchenko, A. I. and Veretin, O. L. (2025) High-precision numerical evaluation of Lauricella functions. NUCLEAR PHYSICS B, 1018: 116994. ISSN 0550-3213, 1873-1562
Full text not available from this repository. (Request a copy)Abstract
We present a method for high-precision numerical evaluations of Lauricella functions whose indices are linearly dependent on some parameter epsilon 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 epsilon dependence of the result is reconstructed from the evaluations of given Lauricella functions at specific numerical values of epsilon, which, in addition, allows for efficient parallel implementation. The method has been implemented in the PrecisionLauricella package, written in Wolfram Mathematica language.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GENERALIZED HYPERGEOMETRIC-FUNCTIONS; MATHEMATICA-BASED PACKAGES; ANALYTIC CONTINUATION; DIFFERENTIAL REDUCTION; LOOP INTEGRALS; FEYNMAN DIAGRAMS; EPSILON EXPANSION; MASTER INTEGRALS; F-D; HYPERDIRE; Hypergeometric functions of many variables; Lauricella functions; High-precision numerical evaluation; Analytic continuation |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Jul 2026 08:23 |
| Last Modified: | 14 Jul 2026 08:23 |
| URI: | https://pred.uni-regensburg.de/id/eprint/66930 |
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