{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6WBLSPAXOVEYUGT7X4EFWCZP6V","short_pith_number":"pith:6WBLSPAX","schema_version":"1.0","canonical_sha256":"f582b93c1775498a1a7fbf085b0b2ff564f2b225e48f35b677db9ed9c7c608d0","source":{"kind":"arxiv","id":"1707.06275","version":2},"attestation_state":"computed","paper":{"title":"On integral representations and asymptotics of some hypergeometric functions in two variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Malte Henkel, Sascha Wald","submitted_at":"2017-07-19T19:58:52Z","abstract_excerpt":"The leading asymptotic behaviour of the Humbert functions $\\Phi_2$, $\\Phi_3$, $\\Xi_2$ of two variables is found, when the absolute values of the two independent variables become simultaneosly large. New integral representations of these functions are given. These are re-expressed as inverse Laplace transformations and the asymptotics is then found from a Tauberian theorem. Some integrals of the Humbert functions are also analysed."},"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":"1707.06275","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-07-19T19:58:52Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.CA","math.MP"],"title_canon_sha256":"7227d9e1d591833ec0f6114b7fdc15275e1e8ca4d4b17b2fea471d884d190931","abstract_canon_sha256":"cb1f8774c097b76a8d7114f664e7fb590018bd5383b76eeb770c87fb64e4d5f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:41.984385Z","signature_b64":"9Q70gSbG/muJoVZfIPsh9bk3I374E5kJlbJvQn0pAcTURfimYsJnhZS1vGIhTD2SXEY/HAYTAQL0i6j29f8LAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f582b93c1775498a1a7fbf085b0b2ff564f2b225e48f35b677db9ed9c7c608d0","last_reissued_at":"2026-05-18T00:25:41.983728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:41.983728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On integral representations and asymptotics of some hypergeometric functions in two variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Malte Henkel, Sascha Wald","submitted_at":"2017-07-19T19:58:52Z","abstract_excerpt":"The leading asymptotic behaviour of the Humbert functions $\\Phi_2$, $\\Phi_3$, $\\Xi_2$ of two variables is found, when the absolute values of the two independent variables become simultaneosly large. New integral representations of these functions are given. These are re-expressed as inverse Laplace transformations and the asymptotics is then found from a Tauberian theorem. Some integrals of the Humbert functions are also analysed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06275","kind":"arxiv","version":2},"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":"1707.06275","created_at":"2026-05-18T00:25:41.983820+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.06275v2","created_at":"2026-05-18T00:25:41.983820+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06275","created_at":"2026-05-18T00:25:41.983820+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/6WBLSPAXOVEYUGT7X4EFWCZP6V","json":"https://pith.science/pith/6WBLSPAXOVEYUGT7X4EFWCZP6V.json","graph_json":"https://pith.science/api/pith-number/6WBLSPAXOVEYUGT7X4EFWCZP6V/graph.json","events_json":"https://pith.science/api/pith-number/6WBLSPAXOVEYUGT7X4EFWCZP6V/events.json","paper":"https://pith.science/paper/6WBLSPAX"},"agent_actions":{"view_html":"https://pith.science/pith/6WBLSPAXOVEYUGT7X4EFWCZP6V","download_json":"https://pith.science/pith/6WBLSPAXOVEYUGT7X4EFWCZP6V.json","view_paper":"https://pith.science/paper/6WBLSPAX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.06275&json=true","fetch_graph":"https://pith.science/api/pith-number/6WBLSPAXOVEYUGT7X4EFWCZP6V/graph.json","fetch_events":"https://pith.science/api/pith-number/6WBLSPAXOVEYUGT7X4EFWCZP6V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6WBLSPAXOVEYUGT7X4EFWCZP6V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6WBLSPAXOVEYUGT7X4EFWCZP6V/action/storage_attestation","attest_author":"https://pith.science/pith/6WBLSPAXOVEYUGT7X4EFWCZP6V/action/author_attestation","sign_citation":"https://pith.science/pith/6WBLSPAXOVEYUGT7X4EFWCZP6V/action/citation_signature","submit_replication":"https://pith.science/pith/6WBLSPAXOVEYUGT7X4EFWCZP6V/action/replication_record"}},"created_at":"2026-05-18T00:25:41.983820+00:00","updated_at":"2026-05-18T00:25:41.983820+00:00"}