{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1994:A2BLAYXBH33METPJLYEGQEDIHP","short_pith_number":"pith:A2BLAYXB","schema_version":"1.0","canonical_sha256":"0682b062e13ef6c24de95e086810683bf3a00ff63022b2087a4defbfbe4d08d1","source":{"kind":"arxiv","id":"math/9404224","version":1},"attestation_state":"computed","paper":{"title":"Explicit representations of biorthogonal polynomials","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Arieh Iserles, Syvert Paul N{\\o}rsett","submitted_at":"1994-04-22T00:00:00Z","abstract_excerpt":"Given a parametrised weight function $\\omega(x,\\mu)$ such that the quotients of its consecutive moments are M\\\"obius maps, it is possible to express the underlying biorthogonal polynomials in a closed form \\cite{IN2}. In the present paper we address ourselves to two related issues. Firstly, we demonstrate that, subject to additional assumptions, every such $\\omega$ obeys (in $x$) a linear differential equation whose solution is a generalized hypergeometric function. Secondly, using a generalization of standard divided differences, we present a new explicit representation of the underlying orth"},"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":"math/9404224","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"1994-04-22T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"09f948dcb0988bd885b4796270ebe0ab205568c1acd1fc1e600e5c522462417d","abstract_canon_sha256":"17c7d573ec2cd724312db0e76469120ac78d169b1477d9ac5ba43f5bbd6b5135"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:23.072283Z","signature_b64":"oxP15aWu+z+hsxqUfaqVzjN9IJfBRvcjHgYxBJ18bzQK3KwVdLN6sEOkdv7Ro2ZCow6ylBaOBzFYMmByXsWxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0682b062e13ef6c24de95e086810683bf3a00ff63022b2087a4defbfbe4d08d1","last_reissued_at":"2026-05-18T01:38:23.071630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:23.071630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit representations of biorthogonal polynomials","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Arieh Iserles, Syvert Paul N{\\o}rsett","submitted_at":"1994-04-22T00:00:00Z","abstract_excerpt":"Given a parametrised weight function $\\omega(x,\\mu)$ such that the quotients of its consecutive moments are M\\\"obius maps, it is possible to express the underlying biorthogonal polynomials in a closed form \\cite{IN2}. In the present paper we address ourselves to two related issues. Firstly, we demonstrate that, subject to additional assumptions, every such $\\omega$ obeys (in $x$) a linear differential equation whose solution is a generalized hypergeometric function. Secondly, using a generalization of standard divided differences, we present a new explicit representation of the underlying orth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9404224","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":"math/9404224","created_at":"2026-05-18T01:38:23.071731+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9404224v1","created_at":"2026-05-18T01:38:23.071731+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9404224","created_at":"2026-05-18T01:38:23.071731+00:00"},{"alias_kind":"pith_short_12","alias_value":"A2BLAYXBH33M","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"A2BLAYXBH33METPJ","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"A2BLAYXB","created_at":"2026-05-18T12:25:47.102015+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/A2BLAYXBH33METPJLYEGQEDIHP","json":"https://pith.science/pith/A2BLAYXBH33METPJLYEGQEDIHP.json","graph_json":"https://pith.science/api/pith-number/A2BLAYXBH33METPJLYEGQEDIHP/graph.json","events_json":"https://pith.science/api/pith-number/A2BLAYXBH33METPJLYEGQEDIHP/events.json","paper":"https://pith.science/paper/A2BLAYXB"},"agent_actions":{"view_html":"https://pith.science/pith/A2BLAYXBH33METPJLYEGQEDIHP","download_json":"https://pith.science/pith/A2BLAYXBH33METPJLYEGQEDIHP.json","view_paper":"https://pith.science/paper/A2BLAYXB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9404224&json=true","fetch_graph":"https://pith.science/api/pith-number/A2BLAYXBH33METPJLYEGQEDIHP/graph.json","fetch_events":"https://pith.science/api/pith-number/A2BLAYXBH33METPJLYEGQEDIHP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A2BLAYXBH33METPJLYEGQEDIHP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A2BLAYXBH33METPJLYEGQEDIHP/action/storage_attestation","attest_author":"https://pith.science/pith/A2BLAYXBH33METPJLYEGQEDIHP/action/author_attestation","sign_citation":"https://pith.science/pith/A2BLAYXBH33METPJLYEGQEDIHP/action/citation_signature","submit_replication":"https://pith.science/pith/A2BLAYXBH33METPJLYEGQEDIHP/action/replication_record"}},"created_at":"2026-05-18T01:38:23.071731+00:00","updated_at":"2026-05-18T01:38:23.071731+00:00"}