{"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/on-the-reduction-of-generalized","title":"On the reduction of generalized polylogarithms to $\\text{Li}_n$ and $\\text{Li}_{2,2}$ and on the evaluation thereof","arxiv_id":"1601.02649","date":"2016-01-11","proceeding":null,"authors":["Hjalte Frellesvig","Damiano Tommasini","Christopher Wever"],"abstract":"We give expressions for all generalized polylogarithms up to weight four in terms of the functions log, $\\text{Li}_n$, and $\\text{Li}_{2,2}$, valid for arbitrary complex variables. Furthermore we provide algorithms for manipulation and numerical evaluation of $\\text{Li}_n$ and $\\text{Li}_{2,2}$, and add codes in Mathematica and C++ implementing the results. With these results we calculate a number of previously unknown integrals, which we add in App. C.","url_abs":"https://arxiv.org/abs/1601.02649v3","url_pdf":"https://arxiv.org/pdf/1601.02649v3.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":"on-the-reduction-of-generalized","repo_url":"https://bitbucket.org/SebastianKirchner/lisk","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"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}