{"paper":{"title":"A Characterization of Askey-Wilson polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kerstin Jordaan, Maurice Kenfack Nangho","submitted_at":"2017-11-09T12:28:15Z","abstract_excerpt":"We show that the only monic orthogonal polynomials $\\{P_n\\}_{n=0}^{\\infty}$ that satisfy $$\\pi(x)\\mathcal{D}_{q}^2P_{n}(x)=\\sum_{j=-2}^{2}a_{n,n+j}P_{n+j}(x),\\; x=\\cos\\theta,\\;~ a_{n,n-2}\\neq 0,~ n=2,3,\\dots,$$ where $\\pi(x)$ is a polynomial of degree at most $4$ and $\\mathcal{D}_{q}$ is the Askey-Wilson operator, are Askey-Wilson polynomials and their special or limiting cases. This completes and proves a conjecture by Ismail concerning a structure relation satisfied by Askey-Wilson polynomials. We use the structure relation to derive upper bounds for the smallest zero and lower bounds for th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03349","kind":"arxiv","version":3},"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"}