{"paper":{"title":"A limit $q=-1$ for the big q-Jacobi polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexei Zhedanov, Luc Vinet","submitted_at":"2010-11-05T15:19:48Z","abstract_excerpt":"We study a new family of \"classical\" orthogonal polynomials, here called big -1 Jacobi polynomials, which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with differential operators of Dunkl-type. These polynomials can be obtained from the big $q$-Jacobi polynomials in the limit $q \\to -1$. An explicit expression of these polynomials in terms of Gauss' hypergeometric functions is found. The big -1 Jacobi polynomials are orthogonal on the union of two symmetric intervals of the real axis. We show that the big -1 Jacobi polynomials can be obtained from the Bannai-Ito poly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1429","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"}