{"paper":{"title":"A Relativistic Conical Function and its Whittaker Limits","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA","nlin.SI"],"primary_cat":"math.CA","authors_text":"Simon Ruijsenaars","submitted_at":"2011-11-01T05:06:28Z","abstract_excerpt":"In previous work we introduced and studied a function $R(a_{+},a_{-},{\\bf c};v,\\hat{v})$ that is a generalization of the hypergeometric function ${}_2F_1$ and the Askey-Wilson polynomials. When the coupling vector ${\\bf c}\\in{\\mathbb C}^4$ is specialized to $(b,0,0,0)$, $b\\in{\\mathbb C}$, we obtain a function ${\\mathcal R}(a_{+},a_{-},b;v,2\\hat{v})$ that generalizes the conical function specialization of ${}_2F_1$ and the $q$-Gegenbauer polynomials. The function ${\\mathcal R}$ is the joint eigenfunction of four analytic difference operators associated with the relativistic Calogero-Moser syste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0115","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"}