{"paper":{"title":"Matrix Gegenbauer Polynomials: the $2\\times 2$ Fundamental Cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ignacio Zurri\\'an, In\\'es Pacharoni","submitted_at":"2013-09-24T23:19:58Z","abstract_excerpt":"In this paper, we exhibit explicitly a sequence of $2\\times2$ matrix valued orthogonal polynomials with respect to a weight $W_{p,n}$, for any pair of real numbers $p$ and $n$ such that $0<p<n$.\n  The entries of these polynomiales are expressed in terms of the Gegenbauer polynomials $C_k^\\lambda$. Also the corresponding three-term recursion relations are given and we make some studies of the algebra of differential operators associated with the weight $W_{p,n}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6902","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"}