{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:OM3S6HK4T5DB526DHXYWUPLQ33","short_pith_number":"pith:OM3S6HK4","schema_version":"1.0","canonical_sha256":"73372f1d5c9f461eebc33df16a3d70ded1c9c6bcc2290e7ee590d79066c09d9e","source":{"kind":"arxiv","id":"1707.06969","version":1},"attestation_state":"computed","paper":{"title":"Mehler's formulas for the univariate complex Hermite polynomials and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Allal Ghanmi","submitted_at":"2017-07-21T16:41:21Z","abstract_excerpt":"We give two widest Mehler's formulas for the univariate complex Hermite polynomials $H_{m,n}^\\nu$, by performing double summations involving the products $u^m H_{m,n}^\\nu (z,\\overline{z}) \\overline{H_{m,n}^\\nu (w,\\overline{w})}$ and $u^m v^n H_{m,n}^\\nu (z,\\overline{z}) \\overline{H_{m,n}^{\\nu'} (w,\\overline{w})}$. They can be seen as the complex analogues of the classical Mehler's formula for the real Hermite polynomials. The proof of the first one is based on a generating function giving rise to the reproducing kernel of the generalized Bargmann space of level $m$. The second Mehler's formula"},"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":"1707.06969","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-07-21T16:41:21Z","cross_cats_sorted":[],"title_canon_sha256":"4f851a03466406281e067db1d6a49c29d2311cc5dce4baf1ea7e228d7873e20d","abstract_canon_sha256":"75b271b90bf30854603ec289516c9d5c644bd46728fd0b22d564c22b42ac658b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:34.730163Z","signature_b64":"PY04YVf9dWLjQOsXVd+e9esMN5sRpZ6QYdejFDBzDbely7EeUY2m1qRjhKT3kkXGWKskQPgLmPMVD6cTo0hgBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73372f1d5c9f461eebc33df16a3d70ded1c9c6bcc2290e7ee590d79066c09d9e","last_reissued_at":"2026-05-18T00:23:34.729335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:34.729335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mehler's formulas for the univariate complex Hermite polynomials and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Allal Ghanmi","submitted_at":"2017-07-21T16:41:21Z","abstract_excerpt":"We give two widest Mehler's formulas for the univariate complex Hermite polynomials $H_{m,n}^\\nu$, by performing double summations involving the products $u^m H_{m,n}^\\nu (z,\\overline{z}) \\overline{H_{m,n}^\\nu (w,\\overline{w})}$ and $u^m v^n H_{m,n}^\\nu (z,\\overline{z}) \\overline{H_{m,n}^{\\nu'} (w,\\overline{w})}$. They can be seen as the complex analogues of the classical Mehler's formula for the real Hermite polynomials. The proof of the first one is based on a generating function giving rise to the reproducing kernel of the generalized Bargmann space of level $m$. The second Mehler's formula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06969","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.06969","created_at":"2026-05-18T00:23:34.729488+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.06969v1","created_at":"2026-05-18T00:23:34.729488+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06969","created_at":"2026-05-18T00:23:34.729488+00:00"},{"alias_kind":"pith_short_12","alias_value":"OM3S6HK4T5DB","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"OM3S6HK4T5DB526D","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"OM3S6HK4","created_at":"2026-05-18T12:31:34.259226+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/OM3S6HK4T5DB526DHXYWUPLQ33","json":"https://pith.science/pith/OM3S6HK4T5DB526DHXYWUPLQ33.json","graph_json":"https://pith.science/api/pith-number/OM3S6HK4T5DB526DHXYWUPLQ33/graph.json","events_json":"https://pith.science/api/pith-number/OM3S6HK4T5DB526DHXYWUPLQ33/events.json","paper":"https://pith.science/paper/OM3S6HK4"},"agent_actions":{"view_html":"https://pith.science/pith/OM3S6HK4T5DB526DHXYWUPLQ33","download_json":"https://pith.science/pith/OM3S6HK4T5DB526DHXYWUPLQ33.json","view_paper":"https://pith.science/paper/OM3S6HK4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.06969&json=true","fetch_graph":"https://pith.science/api/pith-number/OM3S6HK4T5DB526DHXYWUPLQ33/graph.json","fetch_events":"https://pith.science/api/pith-number/OM3S6HK4T5DB526DHXYWUPLQ33/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OM3S6HK4T5DB526DHXYWUPLQ33/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OM3S6HK4T5DB526DHXYWUPLQ33/action/storage_attestation","attest_author":"https://pith.science/pith/OM3S6HK4T5DB526DHXYWUPLQ33/action/author_attestation","sign_citation":"https://pith.science/pith/OM3S6HK4T5DB526DHXYWUPLQ33/action/citation_signature","submit_replication":"https://pith.science/pith/OM3S6HK4T5DB526DHXYWUPLQ33/action/replication_record"}},"created_at":"2026-05-18T00:23:34.729488+00:00","updated_at":"2026-05-18T00:23:34.729488+00:00"}