{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WZOV2SK5S7VZHNWPPXYPZAW743","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ac7686aa133dd059f52a13ae44cae018125705ab2b893aa58855fa8bf107cbc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-07T16:49:52Z","title_canon_sha256":"ae7e8d6d158b91155b0c2544839a1fb015c515568c61a923d18528b92100bc0d"},"schema_version":"1.0","source":{"id":"1711.02603","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02603","created_at":"2026-05-18T00:31:07Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02603v1","created_at":"2026-05-18T00:31:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02603","created_at":"2026-05-18T00:31:07Z"},{"alias_kind":"pith_short_12","alias_value":"WZOV2SK5S7VZ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WZOV2SK5S7VZHNWP","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WZOV2SK5","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:d07ab6a6720414f8e8683c5d03d0d9247daf4c47372aaeecaaa1b3eb7816d35a","target":"graph","created_at":"2026-05-18T00:31:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the class $\\mathcal{E}_t(Y)$ of Appell polynomials whose generating function is given by means of a real power $t$ of the moment generating function of a certain random variable $Y$. For such polynomials, we obtain explicit expressions depending on the moments of $Y$. It turns out that various kinds of generalizations of Bernoulli and Apostol-Euler polynomials belong to $\\mathcal{E}_t(Y)$ and can be written and investigated in a unified way. In particular, explicit expression for such polynomials can be given in terms of suitable probabilistic generalizations of the Stirling number","authors_text":"Alberto Lekuona, Jos\\'e A. Adell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-07T16:49:52Z","title":"Explicit expressions for a certain class of Appell polynomials. A probabilistic approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02603","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:21db854f40e16b48c20bdb43ce0ddc4b5893573a4a5dfb9f4210855114068dbe","target":"record","created_at":"2026-05-18T00:31:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ac7686aa133dd059f52a13ae44cae018125705ab2b893aa58855fa8bf107cbc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-07T16:49:52Z","title_canon_sha256":"ae7e8d6d158b91155b0c2544839a1fb015c515568c61a923d18528b92100bc0d"},"schema_version":"1.0","source":{"id":"1711.02603","kind":"arxiv","version":1}},"canonical_sha256":"b65d5d495d97eb93b6cf7df0fc82dfe6e2938969cc816cbccbc3ba89be3026a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b65d5d495d97eb93b6cf7df0fc82dfe6e2938969cc816cbccbc3ba89be3026a4","first_computed_at":"2026-05-18T00:31:07.457753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:07.457753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"za6b4LFXa06kdZhCDXI1Pxw3Y8Aq8I8n9jiGSNvYBDNxZpOEce0nC06/5pRX7QA0i4+p2k+WcXDgBH1qA03hBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:07.458421Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02603","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21db854f40e16b48c20bdb43ce0ddc4b5893573a4a5dfb9f4210855114068dbe","sha256:d07ab6a6720414f8e8683c5d03d0d9247daf4c47372aaeecaaa1b3eb7816d35a"],"state_sha256":"a9c8d7bdb0370a583b2de5fa5ed63f07dd623d22292a3c9f92796d10adc8747f"}