{"paper":{"title":"Zeros of Quasi-Orthogonal Jacobi Polynomials","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kathy Driver, Kerstin Jordaan","submitted_at":"2015-10-29T08:34:57Z","abstract_excerpt":"We consider interlacing properties satisfied by the zeros of Jacobi polynomials in quasi-orthogonal sequences characterised by $\\alpha>-1$, $-2<\\beta<-1$. We give necessary and sufficient conditions under which a conjecture by Askey, that the zeros of Jacobi polynomials $P_n^{(\\alpha, \\beta)}$ and $P_{n}^{(\\alpha,\\beta+2)}$ are interlacing, holds when the parameters $\\alpha$ and $\\beta$ are in the range $\\alpha>-1$ and $-2<\\beta<-1$. We prove that the zeros of $P_n^{(\\alpha, \\beta)}$ and $P_{n+1}^{(\\alpha,\\beta)}$ do not interlace for any $n\\in\\mathbb{N}$, $n\\geq2$ and any fixed $\\alpha$, $\\be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08599","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}