{"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/closed-form-expressions-for-certain-improper","title":"Closed Form Expressions for Certain Improper Integrals of Mathematical Physics","arxiv_id":"2301.13436","date":"2023-01-31","proceeding":null,"authors":["B. Ananthanarayan","Tanay Pathak","Kartik Sharma"],"abstract":"We present new closed-form expressions for certain improper integrals of Mathematical Physics such as certain Ising, Box, and Associated integrals. The techniques we employ here include (a) the Method of Brackets and its modifications and suitable extensions to obtain the Mellin-Barnes representation. (b) The evaluation of the resulting Mellin-Barnes representations via the recently discovered Conic Hull method via the automated package $\\textit{MBConichulls.wl}$. Finally, the analytic continuations of these series solutions are then produced using the automated package \\texttt{Olsson.wl}, based on the method of Olsson. Thus, combining all these recent advances allows for closed-form evaluation of the hitherto unknown $B_3(s)$, $B_4(s)$, and related integrals in terms of multivariable hypergeometric functions. Along the way, we also discuss certain complications while using the Original Method of Brackets for these evaluations and how to rectify them. The interesting cases of $C_{5,k}$ are also studied. It is not yet fully resolved for the reasons we discuss in this paper.","url_abs":"https://arxiv.org/abs/2301.13436v2","url_pdf":"https://arxiv.org/pdf/2301.13436v2.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":"closed-form-expressions-for-certain-improper","repo_url":"https://github.com/tanaypathak-17/improper-integrals","is_official":1,"mentioned_in_paper":1,"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}