{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:74JG7GTHLGEWKAYJNFZ5XHYP5Z","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":"76884c74f1107806bf19895cf82339bc48f8ba7c32b1de85e8aea962457d152c","cross_cats_sorted":["math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-04-23T20:57:43Z","title_canon_sha256":"03575f2ab20b4198169fb24808115c23ea2e199a6a275a13cb5a952de328bada"},"schema_version":"1.0","source":{"id":"1704.06981","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06981","created_at":"2026-05-18T00:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06981v1","created_at":"2026-05-18T00:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06981","created_at":"2026-05-18T00:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"74JG7GTHLGEW","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"74JG7GTHLGEWKAYJ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"74JG7GTH","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:c58d2dbd504bde8e91dfd7c7c33767f3e54dbbd66d3ce5f2d74a184fc26301de","target":"graph","created_at":"2026-05-18T00:45:21Z","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 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.","authors_text":"Jan Derezi\\'nski, Maciej Karczmarczyk","cross_cats":["math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-04-23T20:57:43Z","title":"Equations of hypergeometric type in the degenerate case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06981","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":"sha256:3cab9d7a43192cfed59677de7b88421e952e0e105a49c768bdd61bcf43656949","target":"record","created_at":"2026-05-18T00:45:21Z","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":"76884c74f1107806bf19895cf82339bc48f8ba7c32b1de85e8aea962457d152c","cross_cats_sorted":["math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-04-23T20:57:43Z","title_canon_sha256":"03575f2ab20b4198169fb24808115c23ea2e199a6a275a13cb5a952de328bada"},"schema_version":"1.0","source":{"id":"1704.06981","kind":"arxiv","version":1}},"canonical_sha256":"ff126f9a6759896503096973db9f0fee7f980f2b173582fdd7a4374d7b623916","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff126f9a6759896503096973db9f0fee7f980f2b173582fdd7a4374d7b623916","first_computed_at":"2026-05-18T00:45:21.778107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:21.778107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6kpxrTExmqdfQPj8PWnqon6c3ZezTl0jSuXCkTwy7NPxVbaQuH8jWqCqx7HHLEaaq7ps8nfXhdafIc/tCLBvBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:21.778735Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06981","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cab9d7a43192cfed59677de7b88421e952e0e105a49c768bdd61bcf43656949","sha256:c58d2dbd504bde8e91dfd7c7c33767f3e54dbbd66d3ce5f2d74a184fc26301de"],"state_sha256":"9d68ed24ee7f2a98201fd6a2fd7b64053bf96ca931362184d10e6b08b97dd598"}