{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:74JG7GTHLGEWKAYJNFZ5XHYP5Z","short_pith_number":"pith:74JG7GTH","schema_version":"1.0","canonical_sha256":"ff126f9a6759896503096973db9f0fee7f980f2b173582fdd7a4374d7b623916","source":{"kind":"arxiv","id":"1704.06981","version":1},"attestation_state":"computed","paper":{"title":"Equations of hypergeometric type in the degenerate case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Jan Derezi\\'nski, Maciej Karczmarczyk","submitted_at":"2017-04-23T20:57:43Z","abstract_excerpt":"We consider the three most important equations of hypergeometric type, ${}_2F_1$, ${}_1F_1$ and ${}_1F_0$, in the so-called degenerate case. In this case one of the parameters, usually denoted $c$, is an integer and the standard basis of solutions consists of a hypergeometric-type function and a function with a logarithmic singularity. This article is devoted to a thorough analysis of the latter solution to all three equations."},"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":"1704.06981","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-04-23T20:57:43Z","cross_cats_sorted":["math.CA","math.MP"],"title_canon_sha256":"03575f2ab20b4198169fb24808115c23ea2e199a6a275a13cb5a952de328bada","abstract_canon_sha256":"76884c74f1107806bf19895cf82339bc48f8ba7c32b1de85e8aea962457d152c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:21.778735Z","signature_b64":"6kpxrTExmqdfQPj8PWnqon6c3ZezTl0jSuXCkTwy7NPxVbaQuH8jWqCqx7HHLEaaq7ps8nfXhdafIc/tCLBvBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff126f9a6759896503096973db9f0fee7f980f2b173582fdd7a4374d7b623916","last_reissued_at":"2026-05-18T00:45:21.778107Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:21.778107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equations of hypergeometric type in the degenerate case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Jan Derezi\\'nski, Maciej Karczmarczyk","submitted_at":"2017-04-23T20:57:43Z","abstract_excerpt":"We consider the three most important equations of hypergeometric type, ${}_2F_1$, ${}_1F_1$ and ${}_1F_0$, in the so-called degenerate case. In this case one of the parameters, usually denoted $c$, is an integer and the standard basis of solutions consists of a hypergeometric-type function and a function with a logarithmic singularity. This article is devoted to a thorough analysis of the latter solution to all three equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06981","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":"1704.06981","created_at":"2026-05-18T00:45:21.778196+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.06981v1","created_at":"2026-05-18T00:45:21.778196+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06981","created_at":"2026-05-18T00:45:21.778196+00:00"},{"alias_kind":"pith_short_12","alias_value":"74JG7GTHLGEW","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"74JG7GTHLGEWKAYJ","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"74JG7GTH","created_at":"2026-05-18T12:31:03.183658+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/74JG7GTHLGEWKAYJNFZ5XHYP5Z","json":"https://pith.science/pith/74JG7GTHLGEWKAYJNFZ5XHYP5Z.json","graph_json":"https://pith.science/api/pith-number/74JG7GTHLGEWKAYJNFZ5XHYP5Z/graph.json","events_json":"https://pith.science/api/pith-number/74JG7GTHLGEWKAYJNFZ5XHYP5Z/events.json","paper":"https://pith.science/paper/74JG7GTH"},"agent_actions":{"view_html":"https://pith.science/pith/74JG7GTHLGEWKAYJNFZ5XHYP5Z","download_json":"https://pith.science/pith/74JG7GTHLGEWKAYJNFZ5XHYP5Z.json","view_paper":"https://pith.science/paper/74JG7GTH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.06981&json=true","fetch_graph":"https://pith.science/api/pith-number/74JG7GTHLGEWKAYJNFZ5XHYP5Z/graph.json","fetch_events":"https://pith.science/api/pith-number/74JG7GTHLGEWKAYJNFZ5XHYP5Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/74JG7GTHLGEWKAYJNFZ5XHYP5Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/74JG7GTHLGEWKAYJNFZ5XHYP5Z/action/storage_attestation","attest_author":"https://pith.science/pith/74JG7GTHLGEWKAYJNFZ5XHYP5Z/action/author_attestation","sign_citation":"https://pith.science/pith/74JG7GTHLGEWKAYJNFZ5XHYP5Z/action/citation_signature","submit_replication":"https://pith.science/pith/74JG7GTHLGEWKAYJNFZ5XHYP5Z/action/replication_record"}},"created_at":"2026-05-18T00:45:21.778196+00:00","updated_at":"2026-05-18T00:45:21.778196+00:00"}