{"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/a-partial-sum-deformation-for-a-family-of","title":"A partial-sum deformation for a family of orthogonal polynomials","arxiv_id":"2409.00261","date":"2024-08-30","proceeding":null,"authors":["Erik Koelink","Pablo Román","Wadim Zudilin"],"abstract":"There are several questions one may ask about polynomials $q_m(x)=q_m(x;t)=\\sum_{n=0}^mt^mp_n(x)$ attached to a family of orthogonal polynomials $\\{p_n(x)\\}_{n\\ge0}$. In this note we draw attention to the naturalness of this partial-sum deformation and related beautiful structures. In particular, we investigate the location and distribution of zeros of $q_m(x;t)$ in the case of varying real parameter $t$.","url_abs":"https://arxiv.org/abs/2409.00261v2","url_pdf":"https://arxiv.org/pdf/2409.00261v2.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":"a-partial-sum-deformation-for-a-family-of","repo_url":"https://github.com/pabloroman-unc/partial-sums","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}