{"paper":{"title":"Limit transition between hypergeometric functions of type BC and type A","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CA","authors_text":"Margit R\\\"osler, Michael Voit, Tom Koornwinder","submitted_at":"2012-07-02T19:57:43Z","abstract_excerpt":"Let $F_{BC}(\\lambda,k;t)$ be the Heckman-Opdam hypergeometric function of type BC with multiplicities $k=(k_1,k_2,k_3)$ and weighted half sum $\\rho(k)$ of positive roots. We prove that $F_{BC}(\\lambda+\\rho(k),k;t)$ converges for $k_1+k_2\\to\\infty$ and $k_1/k_2\\to \\infty$ to a function of type A for $t\\in\\b R^n$ and $\\lambda\\in\\b C^n$. This limit is obtained from a corresponding result for Jacobi polynomials of type BC, which is proven for a slightly more general limit behavior of the multiplicities, using an explicit representation of Jacobi polynomials in terms of Jack polynomials. Our limits"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0487","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"}