{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:LJFOQT4HPMEZHIESM4TZ5PTAOK","short_pith_number":"pith:LJFOQT4H","schema_version":"1.0","canonical_sha256":"5a4ae84f877b0993a09267279ebe60729079654689060f4c6537416f73ed96de","source":{"kind":"arxiv","id":"0910.3087","version":2},"attestation_state":"computed","paper":{"title":"Parametric transformations between the Heun and Gauss hypergeometric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Galina Filipuk, Raimundas Vidunas","submitted_at":"2009-10-16T11:35:08Z","abstract_excerpt":"The hypergeometric and Heun functions are classical special functions. Transformation formulas between them are commonly induced by pull-back transformations of their differential equations, with respect to some coverings P1-to-P1. This gives expressions of Heun functions in terms of better understood hypergeometric functions. This article presents the list of hypergeometric-to-Heun pull-back transformations with a free continuous parameter, and illustrates most of them by a Heun-to-hypergeometric reduction formula. In total, 61 parametric transformations exist, of maximal degree 12."},"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":"0910.3087","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-10-16T11:35:08Z","cross_cats_sorted":[],"title_canon_sha256":"28352a020a96a4d811ed2c01eb4e5664ff8e600a540125843e8d3526cb4be3aa","abstract_canon_sha256":"7e72c17ac8a81a7e81d4123aa31b0c5d7cd269bba59a3622e1707026d22a9929"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:33.920222Z","signature_b64":"HvuYzdPS0/MerStZccwMa4swIl0phafKZqNTUFsavVkDOgSewyeqShfPYFony1vODv9FCtBMtlPm4ZDq6MdjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a4ae84f877b0993a09267279ebe60729079654689060f4c6537416f73ed96de","last_reissued_at":"2026-05-18T03:11:33.919702Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:33.919702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parametric transformations between the Heun and Gauss hypergeometric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Galina Filipuk, Raimundas Vidunas","submitted_at":"2009-10-16T11:35:08Z","abstract_excerpt":"The hypergeometric and Heun functions are classical special functions. Transformation formulas between them are commonly induced by pull-back transformations of their differential equations, with respect to some coverings P1-to-P1. This gives expressions of Heun functions in terms of better understood hypergeometric functions. This article presents the list of hypergeometric-to-Heun pull-back transformations with a free continuous parameter, and illustrates most of them by a Heun-to-hypergeometric reduction formula. In total, 61 parametric transformations exist, of maximal degree 12."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.3087","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":"0910.3087","created_at":"2026-05-18T03:11:33.919772+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.3087v2","created_at":"2026-05-18T03:11:33.919772+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.3087","created_at":"2026-05-18T03:11:33.919772+00:00"},{"alias_kind":"pith_short_12","alias_value":"LJFOQT4HPMEZ","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"LJFOQT4HPMEZHIES","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"LJFOQT4H","created_at":"2026-05-18T12:26:00.592388+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/LJFOQT4HPMEZHIESM4TZ5PTAOK","json":"https://pith.science/pith/LJFOQT4HPMEZHIESM4TZ5PTAOK.json","graph_json":"https://pith.science/api/pith-number/LJFOQT4HPMEZHIESM4TZ5PTAOK/graph.json","events_json":"https://pith.science/api/pith-number/LJFOQT4HPMEZHIESM4TZ5PTAOK/events.json","paper":"https://pith.science/paper/LJFOQT4H"},"agent_actions":{"view_html":"https://pith.science/pith/LJFOQT4HPMEZHIESM4TZ5PTAOK","download_json":"https://pith.science/pith/LJFOQT4HPMEZHIESM4TZ5PTAOK.json","view_paper":"https://pith.science/paper/LJFOQT4H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.3087&json=true","fetch_graph":"https://pith.science/api/pith-number/LJFOQT4HPMEZHIESM4TZ5PTAOK/graph.json","fetch_events":"https://pith.science/api/pith-number/LJFOQT4HPMEZHIESM4TZ5PTAOK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LJFOQT4HPMEZHIESM4TZ5PTAOK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LJFOQT4HPMEZHIESM4TZ5PTAOK/action/storage_attestation","attest_author":"https://pith.science/pith/LJFOQT4HPMEZHIESM4TZ5PTAOK/action/author_attestation","sign_citation":"https://pith.science/pith/LJFOQT4HPMEZHIESM4TZ5PTAOK/action/citation_signature","submit_replication":"https://pith.science/pith/LJFOQT4HPMEZHIESM4TZ5PTAOK/action/replication_record"}},"created_at":"2026-05-18T03:11:33.919772+00:00","updated_at":"2026-05-18T03:11:33.919772+00:00"}