{"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/definite-sums-as-solutions-of-linear","title":"Definite Sums as Solutions of Linear Recurrences With Polynomial Coefficients","arxiv_id":"1804.02964","date":"2018-04-09","proceeding":null,"authors":["Marko Petkovšek"],"abstract":"We present an algorithm which, given a linear recurrence operator $L$ with polynomial coefficients, $m \\in \\mathbb{N}\\setminus\\{0\\}$, $a_1,a_2,\\ldots,a_m \\in \\mathbb{N}\\setminus\\{0\\}$ and $b_1,b_2,\\ldots,b_m \\in \\mathbb{K}$, returns a linear recurrence operator $L'$ with rational coefficients such that for every sequence $h$, \\[ L\\left(\\sum_{k=0}^\\infty \\prod_{i=1}^m \\binom{a_i n + b_i}{k} h_k\\right) = 0 \\] if and only if $L' h = 0$.","url_abs":"https://arxiv.org/abs/1804.02964v1","url_pdf":"https://arxiv.org/pdf/1804.02964v1.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":"definite-sums-as-solutions-of-linear","repo_url":"https://github.com/antonio-jp/pseries_basis","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}