{"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/analytic-continuations-of-the-horn-h-1-and-h","title":"Analytic continuations of the Horn $H_1$ and $H_5$ functions","arxiv_id":"2210.17370","date":"2022-10-31","proceeding":null,"authors":["Souvik Bera","Tanay Pathak"],"abstract":"The analytic continuations (ACs) of the double variable Horn $H_1$ and $H_5$ functions have been derived for the first time using the automated symbolic $\\textit{Mathematica}$ package $\\texttt{Olsson.wl}$. The use of Pfaff-Euler transformations have been emphasised to derive AC to cover regions which are otherwise not possible. The corresponding region of convergence (ROC) is obtained using its companion package $\\texttt{ROC2.wl}$. A $\\textit{Mathematica}$ package $\\texttt{HornH1H5.wl}$, containing all the derived ACs and the associated ROCs, along with a demonstration file of the same is made publicly available in https://github.com/souvik5151/Horn_H1_H5 .","url_abs":"https://arxiv.org/abs/2210.17370v3","url_pdf":"https://arxiv.org/pdf/2210.17370v3.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":"analytic-continuations-of-the-horn-h-1-and-h","repo_url":"https://github.com/souvik5151/horn_h1_h5","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}