{"paper":{"title":"Differential operators, radial parts and a one-parameter family of hypergeometric functions of type BC","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"A. Pasquale, E. K. Narayanan","submitted_at":"2017-04-30T07:00:03Z","abstract_excerpt":"We introduce the symmetric (respectively, non-symmetric) $\\tau_{-\\ell}-$hypergeometric functions associated with a root system of type $BC$ as joint eigenfunctions of a commutative algebra of differential (respectively, differential-reflection) operators. Under certain conditions on the real parameter $\\ell$, we derive their properties (positivity, estimates, asymptotics and boundedness) by establishing the analogous properties for the Heckman-Opdam (symmetric and non-symmetric) hypergeometric functions corresponding to (not necessarily positive) multiplicity functions which are standard."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00277","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"}