{"paper":{"title":"Two families of orthogonal polynomials on the unit circle from basic hypergeometric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Sri Ranga","submitted_at":"2016-11-24T03:59:13Z","abstract_excerpt":"The sequence $\\{\\,_2\\phi_1(q^{-k},q^{b+1};\\,q^{-\\overline{b}-k+1};\\, q, q^{-\\overline{b}+1/2} z)\\}_{k \\geq 0}$ of basic hypergeometric polynomials is known to be orthogonal on the unit circle with respect to the weight function $|(q^{1/2}e^{i\\theta};\\,q)_{\\infty}/(q^{b+1/2}e^{i\\theta};\\,q)_{\\infty}|^2$. This result, where one must take the parameters $q$ and $b$ to be $0 < q < 1$ and $\\Re(b) > -1/2$, is due to P.I. Pastro \\cite{Pastro-1985}. In the present manuscript we deal with the orthogonal polynomials $\\hat{\\Phi}_{n}(b;.)$ and $\\check{\\Phi}_{n}(b;.)$ on the unit circle with respect to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08064","kind":"arxiv","version":4},"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"}