{"paper":{"title":"Nevanlinna extremal measures for polynomials related to $q^{-1}$-Fibonacci polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.CA","authors_text":"Franti\\v{s}ek \\v{S}tampach","submitted_at":"2015-05-04T18:18:35Z","abstract_excerpt":"The aim of this paper is the study of $q^{-1}$-Fibonacci polynomials with $0<q<1$. First, the $q^{-1}$-Fibonacci polynomials are related to a $q$-exponential function which allows an asymptotic analysis to be worked out. Second, related basic orthogonal polynomials are investigated with the emphasis on their orthogonality properties. In particular, a compact formula for the reproducing kernel is obtained that allows to describe all the N-extremal measures of orthogonality in terms of basic hypergeometric functions and their zeros. Two special cases involving $q$-sine and $q$-cosine are discuss"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00742","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"}