{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:HQAMOB52M5J7WSEKY7TJ262GLR","short_pith_number":"pith:HQAMOB52","schema_version":"1.0","canonical_sha256":"3c00c707ba6753fb488ac7e69d7b465c71ba0b64869ff9e4855f6573f8df1866","source":{"kind":"arxiv","id":"1204.0972","version":2},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1204.0972","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-04T15:25:27Z","cross_cats_sorted":[],"title_canon_sha256":"1f89f0dcf185be84a3f9298571294362b110a3573951048089cf21095e15711f","abstract_canon_sha256":"bad65d8015305557f73d9d128c465da9710ff647a4ef60de2e457e15925e85fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:41.410202Z","signature_b64":"I9p4r/XD9+SdGBshFvGRTFEwX/i/46VUO/gvPyDFV2L+nDYLQMRzju7uInSvgDbMhg5NIqqcG5apxRBtERWaBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c00c707ba6753fb488ac7e69d7b465c71ba0b64869ff9e4855f6573f8df1866","last_reissued_at":"2026-05-18T03:07:41.409365Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:41.409365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1204.0972","created_at":"2026-05-18T03:07:41.409496+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.0972v2","created_at":"2026-05-18T03:07:41.409496+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0972","created_at":"2026-05-18T03:07:41.409496+00:00"},{"alias_kind":"pith_short_12","alias_value":"HQAMOB52M5J7","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"HQAMOB52M5J7WSEK","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"HQAMOB52","created_at":"2026-05-18T12:27:09.501522+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HQAMOB52M5J7WSEKY7TJ262GLR","json":"https://pith.science/pith/HQAMOB52M5J7WSEKY7TJ262GLR.json","graph_json":"https://pith.science/api/pith-number/HQAMOB52M5J7WSEKY7TJ262GLR/graph.json","events_json":"https://pith.science/api/pith-number/HQAMOB52M5J7WSEKY7TJ262GLR/events.json","paper":"https://pith.science/paper/HQAMOB52"},"agent_actions":{"view_html":"https://pith.science/pith/HQAMOB52M5J7WSEKY7TJ262GLR","download_json":"https://pith.science/pith/HQAMOB52M5J7WSEKY7TJ262GLR.json","view_paper":"https://pith.science/paper/HQAMOB52","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.0972&json=true","fetch_graph":"https://pith.science/api/pith-number/HQAMOB52M5J7WSEKY7TJ262GLR/graph.json","fetch_events":"https://pith.science/api/pith-number/HQAMOB52M5J7WSEKY7TJ262GLR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HQAMOB52M5J7WSEKY7TJ262GLR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HQAMOB52M5J7WSEKY7TJ262GLR/action/storage_attestation","attest_author":"https://pith.science/pith/HQAMOB52M5J7WSEKY7TJ262GLR/action/author_attestation","sign_citation":"https://pith.science/pith/HQAMOB52M5J7WSEKY7TJ262GLR/action/citation_signature","submit_replication":"https://pith.science/pith/HQAMOB52M5J7WSEKY7TJ262GLR/action/replication_record"}},"created_at":"2026-05-18T03:07:41.409496+00:00","updated_at":"2026-05-18T03:07:41.409496+00:00"}