{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/high-precision-numerical-evaluation-of","title":"High-precision numerical evaluation of Lauricella functions","arxiv_id":"2502.03276","date":"2025-02-05","proceeding":null,"authors":["M. A. Bezuglov","B. A. Kniehl","A. I. Onishchenko","O. L. Veretin"],"abstract":"We present a method for high-precision numerical evaluations of Lauricella functions, whose indices are linearly dependent on some parameter $\\varepsilon$, 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 $\\varepsilon$ dependence of the result is reconstructed from the evaluations of given Lauricella functions at specific numerical values of $\\varepsilon$, which, in addition, allows for efficient parallel implementation. The method has been implemented in the $\\texttt{PrecisionLauricella}$ package, written in Wolfram Mathematica language.","url_abs":"https://arxiv.org/abs/2502.03276v1","url_pdf":"https://arxiv.org/pdf/2502.03276v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"high-precision-numerical-evaluation-of","repo_url":"https://bitbucket.org/BezuglovMaxim/precisionlauricella-package","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}