{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:JB6MPZJ447PQNC5YSUHLEB5ISR","short_pith_number":"pith:JB6MPZJ4","schema_version":"1.0","canonical_sha256":"487cc7e53ce7df068bb8950eb207a8947e53da2dedaa8411950f953c14f20809","source":{"kind":"arxiv","id":"1901.05886","version":1},"attestation_state":"computed","paper":{"title":"A New Summation Formula for WP-Bailey Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"James Mc Laughlin","submitted_at":"2019-01-05T18:16:28Z","abstract_excerpt":"Let $(\\alpha_n(a,k),\\beta_n(a,k))$ be a WP-Bailey pair. Assuming the limits exist, let \\[ (\\alpha_n^*(a),\\beta_n^*(a))_{n\\geq 1} = \\lim_{k \\to 1}\\left(\\alpha_n(a,k),\\frac{\\beta_n(a,k)}{1-k}\\right)_{n\\geq 1} \\] be the \\emph{derived} WP-Bailey pair. By considering a particular limiting case of a transformation due to George Andrews, we derive new basic hypergeometric summation and transformation formulae involving derived WP-Bailey pairs. We then use these formulae to derive new identities for various theta series/products which are expressible in terms of certain types of Lambert series."},"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":"1901.05886","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-05T18:16:28Z","cross_cats_sorted":[],"title_canon_sha256":"e381b151fba5d17e557f7ebb95c55b418b469bfa763bf7100cd497eb562e773c","abstract_canon_sha256":"611a250adbd2c751d3c69254764c8ad3c3bc071e64178db83227ed8fd7020000"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:05.914288Z","signature_b64":"kv1X0z2IS0wyOnS9HWysrj9MZUWNc3U67VVjKAryX/0hg6AgRGVsCA9Y0ybc/6B9+S51loanPNKp2INORoe6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"487cc7e53ce7df068bb8950eb207a8947e53da2dedaa8411950f953c14f20809","last_reissued_at":"2026-05-17T23:56:05.913749Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:05.913749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A New Summation Formula for WP-Bailey Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"James Mc Laughlin","submitted_at":"2019-01-05T18:16:28Z","abstract_excerpt":"Let $(\\alpha_n(a,k),\\beta_n(a,k))$ be a WP-Bailey pair. Assuming the limits exist, let \\[ (\\alpha_n^*(a),\\beta_n^*(a))_{n\\geq 1} = \\lim_{k \\to 1}\\left(\\alpha_n(a,k),\\frac{\\beta_n(a,k)}{1-k}\\right)_{n\\geq 1} \\] be the \\emph{derived} WP-Bailey pair. By considering a particular limiting case of a transformation due to George Andrews, we derive new basic hypergeometric summation and transformation formulae involving derived WP-Bailey pairs. We then use these formulae to derive new identities for various theta series/products which are expressible in terms of certain types of Lambert series."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05886","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":"1901.05886","created_at":"2026-05-17T23:56:05.913836+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.05886v1","created_at":"2026-05-17T23:56:05.913836+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.05886","created_at":"2026-05-17T23:56:05.913836+00:00"},{"alias_kind":"pith_short_12","alias_value":"JB6MPZJ447PQ","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"JB6MPZJ447PQNC5Y","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"JB6MPZJ4","created_at":"2026-05-18T12:33:18.533446+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/JB6MPZJ447PQNC5YSUHLEB5ISR","json":"https://pith.science/pith/JB6MPZJ447PQNC5YSUHLEB5ISR.json","graph_json":"https://pith.science/api/pith-number/JB6MPZJ447PQNC5YSUHLEB5ISR/graph.json","events_json":"https://pith.science/api/pith-number/JB6MPZJ447PQNC5YSUHLEB5ISR/events.json","paper":"https://pith.science/paper/JB6MPZJ4"},"agent_actions":{"view_html":"https://pith.science/pith/JB6MPZJ447PQNC5YSUHLEB5ISR","download_json":"https://pith.science/pith/JB6MPZJ447PQNC5YSUHLEB5ISR.json","view_paper":"https://pith.science/paper/JB6MPZJ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.05886&json=true","fetch_graph":"https://pith.science/api/pith-number/JB6MPZJ447PQNC5YSUHLEB5ISR/graph.json","fetch_events":"https://pith.science/api/pith-number/JB6MPZJ447PQNC5YSUHLEB5ISR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JB6MPZJ447PQNC5YSUHLEB5ISR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JB6MPZJ447PQNC5YSUHLEB5ISR/action/storage_attestation","attest_author":"https://pith.science/pith/JB6MPZJ447PQNC5YSUHLEB5ISR/action/author_attestation","sign_citation":"https://pith.science/pith/JB6MPZJ447PQNC5YSUHLEB5ISR/action/citation_signature","submit_replication":"https://pith.science/pith/JB6MPZJ447PQNC5YSUHLEB5ISR/action/replication_record"}},"created_at":"2026-05-17T23:56:05.913836+00:00","updated_at":"2026-05-17T23:56:05.913836+00:00"}