{"paper":{"title":"Orthogonal sequences constructed from quasi-orthogonal ultraspherical polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kathy Driver, Oksana Bihun","submitted_at":"2019-05-10T17:34:16Z","abstract_excerpt":"Let $\\displaystyle \\{x_{k,n-1}\\} _{k=1}^{n-1}$ and $\\displaystyle \\{x_{k,n}\\} _{k=1}^{n},$ $n \\in \\mathbb{N}$, be two sets of real, distinct points satisfying the interlacing property $ x_{i,n}<x_{i,n-1}< x_{i+1,n}, \\, \\, \\, i = 1,2,\\dots,n-1.$ Wendroff proved that if $p_{n-1}(x) = \\displaystyle \\prod _{k=1}^{n-1} (x-x_{k,n-1})$ and $p_n(x) = \\displaystyle \\prod _{k=1}^n (x-x_{k,n})$, then $p_{n-1}$ and $p_n$ can be embedded in a non-unique monic orthogonal sequence $\\{p_{n}\\} _{n=0}^\\infty. $ We investigate a question raised by Mourad Ismail at OPSFA 2015 as to the nature and properties of or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04276","kind":"arxiv","version":1},"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"}