{"paper":{"title":"On peculiar properties of generating functions of some orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pawe{\\l} J. Szab{\\l}owski","submitted_at":"2012-04-04T15:25:27Z","abstract_excerpt":"We prove that for |x|,|t|<1, -1 <q \\leq1 and n\\geq0: \\Sigma_{i\\geq0}((t^{i})/((q)_{i}))h_{n+i}(x|q) = h_{n}(x|t,q) \\Sigma_{i\\geq0}((t^{i})/((q)_{i}))h_{i}(x|q), where h_{n}(x|q) and h_{n}(x|t,q) are respectively the so called q-Hermite and the big q-Hermite polynomials and (q)_{n} denotes the so called q-Pochhammer symbol. We prove similar equalities involving big q-Hermite and Al-Salam---Chihara (ASC) polynomials and ASC and the so called continuous dual q-Hahn (c2h) polynomials. Moreover we are able to relate in this way some other 'ordinary ' orthogonal polynomials such as e.g. Hermite, Che"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0972","kind":"arxiv","version":2},"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"}