{"paper":{"title":"Exceptional Meixner and Laguerre orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Antonio J. Duran","submitted_at":"2013-10-17T11:31:04Z","abstract_excerpt":"Using Casorati determinants of Meixner polynomials $(m_n^{a,c})_n$, we construct for each pair $\\F=(F_1,F_2)$ of finite sets of positive integers a sequence of polynomials $m_n^{a,c;\\F}$, $n\\in \\sigma_\\F$, which are eigenfunctions of a second order difference operator, where $\\sigma_\\F$ is certain infinite set of nonnegative integers, $\\sigma_\\F \\varsubsetneq \\NN$. When $c$ and $\\F$ satisfy a suitable admissibility condition, we prove that the polynomials $m_n^{a,c;\\F}$, $n\\in \\sigma_\\F$, are actually exceptional Meixner polynomials; that is, in addition, they are orthogonal and complete with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4658","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"}