{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XZWJGUTSVWW53GG54NCDP7E3P5","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":"cd3b007d20ad176b704fba47348257ac858e71eb5f01a9cd804440dde3fd7adb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-16T13:40:43Z","title_canon_sha256":"78c35ecc9c339c52e442961cbf964bb747404c652f08083653285bee3e59a4d8"},"schema_version":"1.0","source":{"id":"1607.04742","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04742","created_at":"2026-05-18T01:10:55Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04742v2","created_at":"2026-05-18T01:10:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04742","created_at":"2026-05-18T01:10:55Z"},{"alias_kind":"pith_short_12","alias_value":"XZWJGUTSVWW5","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XZWJGUTSVWW53GG5","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XZWJGUTS","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:97dba6b713a041a7f3abae558a658c7a01a9274f877d09e9b0d2ca1ce4434277","target":"graph","created_at":"2026-05-18T01:10:55Z","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":"In a previous work ([Eb]), the author proposed a method employing contiguity relations to derive hypergeometric series in closed form. In [Eb], this method was used to derive Gauss's hypergeometric series $_2F_1$ possessing closed forms. Here, we consider the application of this method to Appell's hypergeometetric series $F_1$ and derive several $F_1$ possessing closed forms. Moreover, analyzing these $F_1$, we obtain values of $_2F_1$ with no free parameters. Some of these results provide new examples of algebraic values of $_2F_1$.\n  Key Words and Phrases: Gauss's hypergeometric series, alge","authors_text":"Akihito Ebisu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-16T13:40:43Z","title":"Special values of Gauss's hypergeometric series derived from Appell's series $F_1$ with closed forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04742","kind":"arxiv","version":2},"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:a90f82913506f5cffe232ad8a5fced462767bfb1106d0234c54e7b60a2a1c396","target":"record","created_at":"2026-05-18T01:10:55Z","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":"cd3b007d20ad176b704fba47348257ac858e71eb5f01a9cd804440dde3fd7adb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-16T13:40:43Z","title_canon_sha256":"78c35ecc9c339c52e442961cbf964bb747404c652f08083653285bee3e59a4d8"},"schema_version":"1.0","source":{"id":"1607.04742","kind":"arxiv","version":2}},"canonical_sha256":"be6c935272adaddd98dde34437fc9b7f5fe3c0e6391bd0023b455810d11fdac5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be6c935272adaddd98dde34437fc9b7f5fe3c0e6391bd0023b455810d11fdac5","first_computed_at":"2026-05-18T01:10:55.324024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:55.324024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mSHshxy1Joad2wIGle9oLrVhqVUsY3dsYzU64bmiXFHfD344eGcd1z43RjFTSAPAtGfW4RJ33PoMoqc87uHrBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:55.324456Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04742","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a90f82913506f5cffe232ad8a5fced462767bfb1106d0234c54e7b60a2a1c396","sha256:97dba6b713a041a7f3abae558a658c7a01a9274f877d09e9b0d2ca1ce4434277"],"state_sha256":"f689876c0553f12fd560791edac2b29b6718f7f9c025a0174f5452290b023f83"}