{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4HQQYKWMR75SEBWKKKPRDIYUPX","short_pith_number":"pith:4HQQYKWM","schema_version":"1.0","canonical_sha256":"e1e10c2acc8ffb2206ca529f11a3147dd8a81e17a29139034d5b4061496c8ddd","source":{"kind":"arxiv","id":"1508.01816","version":2},"attestation_state":"computed","paper":{"title":"Kibble-Slepian Formula and Generating Functions for 2$D$ Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Mourad E. H. Ismail, Ruiming Zhang","submitted_at":"2015-08-01T02:25:22Z","abstract_excerpt":"We prove a generalization of the Kibble--Slepian formula (for Hermite polynomials) and its unitary analogue involving the $2$D Hermite polynomials recently proved in \\cite{Ism4}. We derive integral representations for the $2$D Hermite polynomials which are of independent interest. Several new generating functions for $2$D $q$-Hermite polynomials will also be given."},"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":"1508.01816","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-08-01T02:25:22Z","cross_cats_sorted":[],"title_canon_sha256":"4ce44dcbf245dbf0bbda6bf101e49cc75f6e696d05a3a8300c57690722e205bd","abstract_canon_sha256":"fa092d3c91ec6c5da1ed0a2c85ab3709297fe684a885c68637733b2141971dfb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:23.370379Z","signature_b64":"ArJcUW8fPyZjFjA6+EqgeE3sYdPcOya47bCV8SBgy179EYVWL695nljQZEDiNmfev/lCzYzz9YEN7rNJ5XRBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1e10c2acc8ffb2206ca529f11a3147dd8a81e17a29139034d5b4061496c8ddd","last_reissued_at":"2026-05-18T01:15:23.369778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:23.369778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kibble-Slepian Formula and Generating Functions for 2$D$ Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Mourad E. H. Ismail, Ruiming Zhang","submitted_at":"2015-08-01T02:25:22Z","abstract_excerpt":"We prove a generalization of the Kibble--Slepian formula (for Hermite polynomials) and its unitary analogue involving the $2$D Hermite polynomials recently proved in \\cite{Ism4}. We derive integral representations for the $2$D Hermite polynomials which are of independent interest. Several new generating functions for $2$D $q$-Hermite polynomials will also be given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01816","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":"1508.01816","created_at":"2026-05-18T01:15:23.369858+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.01816v2","created_at":"2026-05-18T01:15:23.369858+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01816","created_at":"2026-05-18T01:15:23.369858+00:00"},{"alias_kind":"pith_short_12","alias_value":"4HQQYKWMR75S","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4HQQYKWMR75SEBWK","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4HQQYKWM","created_at":"2026-05-18T12:29:05.191682+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/4HQQYKWMR75SEBWKKKPRDIYUPX","json":"https://pith.science/pith/4HQQYKWMR75SEBWKKKPRDIYUPX.json","graph_json":"https://pith.science/api/pith-number/4HQQYKWMR75SEBWKKKPRDIYUPX/graph.json","events_json":"https://pith.science/api/pith-number/4HQQYKWMR75SEBWKKKPRDIYUPX/events.json","paper":"https://pith.science/paper/4HQQYKWM"},"agent_actions":{"view_html":"https://pith.science/pith/4HQQYKWMR75SEBWKKKPRDIYUPX","download_json":"https://pith.science/pith/4HQQYKWMR75SEBWKKKPRDIYUPX.json","view_paper":"https://pith.science/paper/4HQQYKWM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.01816&json=true","fetch_graph":"https://pith.science/api/pith-number/4HQQYKWMR75SEBWKKKPRDIYUPX/graph.json","fetch_events":"https://pith.science/api/pith-number/4HQQYKWMR75SEBWKKKPRDIYUPX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4HQQYKWMR75SEBWKKKPRDIYUPX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4HQQYKWMR75SEBWKKKPRDIYUPX/action/storage_attestation","attest_author":"https://pith.science/pith/4HQQYKWMR75SEBWKKKPRDIYUPX/action/author_attestation","sign_citation":"https://pith.science/pith/4HQQYKWMR75SEBWKKKPRDIYUPX/action/citation_signature","submit_replication":"https://pith.science/pith/4HQQYKWMR75SEBWKKKPRDIYUPX/action/replication_record"}},"created_at":"2026-05-18T01:15:23.369858+00:00","updated_at":"2026-05-18T01:15:23.369858+00:00"}