{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6XCPSTAGHX7AMD74WYC6PI2A3V","short_pith_number":"pith:6XCPSTAG","schema_version":"1.0","canonical_sha256":"f5c4f94c063dfe060ffcb605e7a340dd56b1df512f9c2cddf75138193042f71e","source":{"kind":"arxiv","id":"1405.2871","version":1},"attestation_state":"computed","paper":{"title":"The Appell hypergeometric expansions of the solutions of the general Heun equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A.M. Ishkhanyan","submitted_at":"2014-05-12T18:33:30Z","abstract_excerpt":"Starting from the equation obeyed by the derivative, we construct several expansions of the solutions of the general Heun equation in terms of the Appell generalized hypergeometric functions of two variables of the fist kind. Several cases when the expansions reduce to ones written in terms of simpler mathematical functions such as the incomplete Beta function or the Gauss hypergeometric function are identified. The conditions for deriving finite-sum solutions via termination of the series are discussed. In general, the coefficients of the expansions obey four-term recurrence relations; howeve"},"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":"1405.2871","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-12T18:33:30Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"e0cfd62559009b552c4fb527172be54d06098925f9252c6c10908b2f27f653a7","abstract_canon_sha256":"d7b6ba11e683ececf45f0c4152e16d21a6b1d723e2e9c8a78137a312a6e39761"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:04.628400Z","signature_b64":"Jf3JYqZep+pyaC4pQ3/HKMLKCBJa6Lj1VfqEppXPXc/mEo4YwY4OMSmoKIqcmySl9gkMJ6I6lVAuuPSpSU39Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5c4f94c063dfe060ffcb605e7a340dd56b1df512f9c2cddf75138193042f71e","last_reissued_at":"2026-05-18T02:52:04.627923Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:04.627923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Appell hypergeometric expansions of the solutions of the general Heun equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A.M. Ishkhanyan","submitted_at":"2014-05-12T18:33:30Z","abstract_excerpt":"Starting from the equation obeyed by the derivative, we construct several expansions of the solutions of the general Heun equation in terms of the Appell generalized hypergeometric functions of two variables of the fist kind. Several cases when the expansions reduce to ones written in terms of simpler mathematical functions such as the incomplete Beta function or the Gauss hypergeometric function are identified. The conditions for deriving finite-sum solutions via termination of the series are discussed. In general, the coefficients of the expansions obey four-term recurrence relations; howeve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2871","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":"1405.2871","created_at":"2026-05-18T02:52:04.628010+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.2871v1","created_at":"2026-05-18T02:52:04.628010+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2871","created_at":"2026-05-18T02:52:04.628010+00:00"},{"alias_kind":"pith_short_12","alias_value":"6XCPSTAGHX7A","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6XCPSTAGHX7AMD74","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6XCPSTAG","created_at":"2026-05-18T12:28:16.859392+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/6XCPSTAGHX7AMD74WYC6PI2A3V","json":"https://pith.science/pith/6XCPSTAGHX7AMD74WYC6PI2A3V.json","graph_json":"https://pith.science/api/pith-number/6XCPSTAGHX7AMD74WYC6PI2A3V/graph.json","events_json":"https://pith.science/api/pith-number/6XCPSTAGHX7AMD74WYC6PI2A3V/events.json","paper":"https://pith.science/paper/6XCPSTAG"},"agent_actions":{"view_html":"https://pith.science/pith/6XCPSTAGHX7AMD74WYC6PI2A3V","download_json":"https://pith.science/pith/6XCPSTAGHX7AMD74WYC6PI2A3V.json","view_paper":"https://pith.science/paper/6XCPSTAG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.2871&json=true","fetch_graph":"https://pith.science/api/pith-number/6XCPSTAGHX7AMD74WYC6PI2A3V/graph.json","fetch_events":"https://pith.science/api/pith-number/6XCPSTAGHX7AMD74WYC6PI2A3V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6XCPSTAGHX7AMD74WYC6PI2A3V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6XCPSTAGHX7AMD74WYC6PI2A3V/action/storage_attestation","attest_author":"https://pith.science/pith/6XCPSTAGHX7AMD74WYC6PI2A3V/action/author_attestation","sign_citation":"https://pith.science/pith/6XCPSTAGHX7AMD74WYC6PI2A3V/action/citation_signature","submit_replication":"https://pith.science/pith/6XCPSTAGHX7AMD74WYC6PI2A3V/action/replication_record"}},"created_at":"2026-05-18T02:52:04.628010+00:00","updated_at":"2026-05-18T02:52:04.628010+00:00"}