{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:WB5OBLJBK7RG5ZO6XVGDZNDUPW","short_pith_number":"pith:WB5OBLJB","schema_version":"1.0","canonical_sha256":"b07ae0ad2157e26ee5debd4c3cb4747dbfa51b31f09588083aadeb8617333529","source":{"kind":"arxiv","id":"1610.09666","version":1},"attestation_state":"computed","paper":{"title":"Generating Function Transformations Related to Polylogarithm Functions and the $k$-Order Harmonic Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Maxie D. Schmidt","submitted_at":"2016-10-30T15:42:14Z","abstract_excerpt":"We define a new class of generating function transformations related to polylogarithm functions, Dirichlet series, and Euler sums. These transformations are given by an infinite sum over the $j^{th}$ derivatives of a sequence generating function and sets of generalized coefficients satisfying a non-triangular recurrence relation in two variables. The generalized transformation coefficients share a number of analogous properties with the Stirling numbers of the second kind and the known harmonic number expansions of the unsigned Stirling numbers of the first kind.\n  We prove a number of propert"},"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":"1610.09666","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-30T15:42:14Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"fda9ecda8651e4271775fa9ea429cbe7875ea1a8420ae837c34dafaf7760da0c","abstract_canon_sha256":"b3df6c9e4200f4db048ca8f7d2b7046daddccbf233fb477b292d59a322da649d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:18.311705Z","signature_b64":"fF85nDl0J/ubdTfsMxRe4gFOT2Kk/lZx+fLrvWvhCDyIWyaZ8u26fhYOL+fv51O64Nbk9pgaelgS/pEa0qjADw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b07ae0ad2157e26ee5debd4c3cb4747dbfa51b31f09588083aadeb8617333529","last_reissued_at":"2026-05-18T00:43:18.310863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:18.310863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generating Function Transformations Related to Polylogarithm Functions and the $k$-Order Harmonic Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Maxie D. Schmidt","submitted_at":"2016-10-30T15:42:14Z","abstract_excerpt":"We define a new class of generating function transformations related to polylogarithm functions, Dirichlet series, and Euler sums. These transformations are given by an infinite sum over the $j^{th}$ derivatives of a sequence generating function and sets of generalized coefficients satisfying a non-triangular recurrence relation in two variables. The generalized transformation coefficients share a number of analogous properties with the Stirling numbers of the second kind and the known harmonic number expansions of the unsigned Stirling numbers of the first kind.\n  We prove a number of propert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09666","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":"1610.09666","created_at":"2026-05-18T00:43:18.311012+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.09666v1","created_at":"2026-05-18T00:43:18.311012+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09666","created_at":"2026-05-18T00:43:18.311012+00:00"},{"alias_kind":"pith_short_12","alias_value":"WB5OBLJBK7RG","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"WB5OBLJBK7RG5ZO6","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"WB5OBLJB","created_at":"2026-05-18T12:30:48.956258+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/WB5OBLJBK7RG5ZO6XVGDZNDUPW","json":"https://pith.science/pith/WB5OBLJBK7RG5ZO6XVGDZNDUPW.json","graph_json":"https://pith.science/api/pith-number/WB5OBLJBK7RG5ZO6XVGDZNDUPW/graph.json","events_json":"https://pith.science/api/pith-number/WB5OBLJBK7RG5ZO6XVGDZNDUPW/events.json","paper":"https://pith.science/paper/WB5OBLJB"},"agent_actions":{"view_html":"https://pith.science/pith/WB5OBLJBK7RG5ZO6XVGDZNDUPW","download_json":"https://pith.science/pith/WB5OBLJBK7RG5ZO6XVGDZNDUPW.json","view_paper":"https://pith.science/paper/WB5OBLJB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.09666&json=true","fetch_graph":"https://pith.science/api/pith-number/WB5OBLJBK7RG5ZO6XVGDZNDUPW/graph.json","fetch_events":"https://pith.science/api/pith-number/WB5OBLJBK7RG5ZO6XVGDZNDUPW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WB5OBLJBK7RG5ZO6XVGDZNDUPW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WB5OBLJBK7RG5ZO6XVGDZNDUPW/action/storage_attestation","attest_author":"https://pith.science/pith/WB5OBLJBK7RG5ZO6XVGDZNDUPW/action/author_attestation","sign_citation":"https://pith.science/pith/WB5OBLJBK7RG5ZO6XVGDZNDUPW/action/citation_signature","submit_replication":"https://pith.science/pith/WB5OBLJBK7RG5ZO6XVGDZNDUPW/action/replication_record"}},"created_at":"2026-05-18T00:43:18.311012+00:00","updated_at":"2026-05-18T00:43:18.311012+00:00"}