{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:LDVUWY4NGCK2ALO64EP3FIVKJS","short_pith_number":"pith:LDVUWY4N","schema_version":"1.0","canonical_sha256":"58eb4b638d3095a02ddee11fb2a2aa4c8a62d139962bd42ae1039d11aa0cd1b0","source":{"kind":"arxiv","id":"1401.8037","version":1},"attestation_state":"computed","paper":{"title":"Identities for generalized Euler polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"C. Vignat, Lin Jiu, Victor H. Moll","submitted_at":"2014-01-31T01:58:02Z","abstract_excerpt":"For $N \\in \\mathbb{N}$, let $T_{N}$ be the Chebyshev polynomial of the first kind. Expressions for the sequence of numbers $p_{\\ell}^{(N)}$, defined as the coefficients in the expansion of $1/T_{N}(1/z)$, are provided. These coefficients give formulas for the classical Euler polynomials in terms of the so-called generalized Euler polynomials. The proofs are based on a probabilistic interpretation of the generalized Euler polynomials recently given by Klebanov et al. Asymptotics of $p_{\\ell}^{(N)}$ are also provided."},"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":"1401.8037","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-31T01:58:02Z","cross_cats_sorted":[],"title_canon_sha256":"456fa96a0e2a08e6080d6cfedc1905f702f6f72ac25c85661cd9f59ecab7479c","abstract_canon_sha256":"5037cfbeeff1c2a434f9f98b2e215a1ae0058fcf70f42775bcaf2511a45d9563"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:36.382218Z","signature_b64":"AFSwue8axAhLwbeh64FENLc80Eoi7bYN3iDtSpbGHNxB+gtk2mM34H9rPHyo2X2tWMAAuX8yiasLGizfiK30Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58eb4b638d3095a02ddee11fb2a2aa4c8a62d139962bd42ae1039d11aa0cd1b0","last_reissued_at":"2026-05-18T03:00:36.381357Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:36.381357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Identities for generalized Euler polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"C. Vignat, Lin Jiu, Victor H. Moll","submitted_at":"2014-01-31T01:58:02Z","abstract_excerpt":"For $N \\in \\mathbb{N}$, let $T_{N}$ be the Chebyshev polynomial of the first kind. Expressions for the sequence of numbers $p_{\\ell}^{(N)}$, defined as the coefficients in the expansion of $1/T_{N}(1/z)$, are provided. These coefficients give formulas for the classical Euler polynomials in terms of the so-called generalized Euler polynomials. The proofs are based on a probabilistic interpretation of the generalized Euler polynomials recently given by Klebanov et al. Asymptotics of $p_{\\ell}^{(N)}$ are also provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.8037","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":"1401.8037","created_at":"2026-05-18T03:00:36.381511+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.8037v1","created_at":"2026-05-18T03:00:36.381511+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.8037","created_at":"2026-05-18T03:00:36.381511+00:00"},{"alias_kind":"pith_short_12","alias_value":"LDVUWY4NGCK2","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"LDVUWY4NGCK2ALO6","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"LDVUWY4N","created_at":"2026-05-18T12:28:38.356838+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/LDVUWY4NGCK2ALO64EP3FIVKJS","json":"https://pith.science/pith/LDVUWY4NGCK2ALO64EP3FIVKJS.json","graph_json":"https://pith.science/api/pith-number/LDVUWY4NGCK2ALO64EP3FIVKJS/graph.json","events_json":"https://pith.science/api/pith-number/LDVUWY4NGCK2ALO64EP3FIVKJS/events.json","paper":"https://pith.science/paper/LDVUWY4N"},"agent_actions":{"view_html":"https://pith.science/pith/LDVUWY4NGCK2ALO64EP3FIVKJS","download_json":"https://pith.science/pith/LDVUWY4NGCK2ALO64EP3FIVKJS.json","view_paper":"https://pith.science/paper/LDVUWY4N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.8037&json=true","fetch_graph":"https://pith.science/api/pith-number/LDVUWY4NGCK2ALO64EP3FIVKJS/graph.json","fetch_events":"https://pith.science/api/pith-number/LDVUWY4NGCK2ALO64EP3FIVKJS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LDVUWY4NGCK2ALO64EP3FIVKJS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LDVUWY4NGCK2ALO64EP3FIVKJS/action/storage_attestation","attest_author":"https://pith.science/pith/LDVUWY4NGCK2ALO64EP3FIVKJS/action/author_attestation","sign_citation":"https://pith.science/pith/LDVUWY4NGCK2ALO64EP3FIVKJS/action/citation_signature","submit_replication":"https://pith.science/pith/LDVUWY4NGCK2ALO64EP3FIVKJS/action/replication_record"}},"created_at":"2026-05-18T03:00:36.381511+00:00","updated_at":"2026-05-18T03:00:36.381511+00:00"}