{"paper":{"title":"Group-theoretical origin of symmetries of hypergeometric class equations and functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CA","authors_text":"Jan Derezi\\'nski","submitted_at":"2019-06-08T19:53:46Z","abstract_excerpt":"We show that properties of hypergeometric class equations and functions become transparent if we derive them from appropriate 2nd order differential equations with constant coefficients. More precisely, properties of the hypergeometric and Gegenbauer equation can be derived from generalized symmetries of the Laplace equation in 4, resp. 3 dimension. Properties of the confluent, resp. Hermite equation can be derived from generalized symmetries of the heat equation in 2, resp. 1 dimension. Finally, the theory of the ${}_1F_1$ equation (equivalent to the Bessel equation) follows from the symmetri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03512","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"}