{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:TNAN4Y6WBCJ6RQXT7VSTSMUPHX","short_pith_number":"pith:TNAN4Y6W","schema_version":"1.0","canonical_sha256":"9b40de63d60893e8c2f3fd6539328f3dea1d24723e5d5d050f36c517d193f775","source":{"kind":"arxiv","id":"1602.00044","version":2},"attestation_state":"computed","paper":{"title":"Bounds for Extreme Zeros of Quasi-orthogonal Ultraspherical Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kathy Driver, Martin E. Muldoon","submitted_at":"2016-01-30T00:26:42Z","abstract_excerpt":"We discuss and compare upper and lower bounds obtained by two different methods for the positive zero of the ultraspherical polynomial $C_{n}^{(\\lambda)}$ that is greater than $1$ when $-3/2 < \\lambda < -1/2.$ Our first approach uses mixed three term recurrence relations and interlacing of zeros while the second approach uses a method going back to Euler and Rayleigh and already applied to Bessel functions and Laguerre and $q$-Laguerre polynomials. We use the bounds obtained by the second method to simplify the proof of the interlacing of the zeros of $(1-x^2)C_{n}^{(\\lambda)}$ and $C_{n+1}^{("},"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":"1602.00044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-30T00:26:42Z","cross_cats_sorted":[],"title_canon_sha256":"6311de3dceea8d3e1e898c1e8be46b3cc914e02fd1abdc952c69a0da78b2906c","abstract_canon_sha256":"d2bac14f0cf2a3a1770ac72aff1fff6be1b6c9e0a60836d250e1389175467390"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:58.606780Z","signature_b64":"odNFr6z/sCsSAOo8MKH2tTXCU/eNcGrQXJMGUhGStUbqbMWrEocZgXgOT1/MbDhFiTiahy4TAO7QG5NoBekUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b40de63d60893e8c2f3fd6539328f3dea1d24723e5d5d050f36c517d193f775","last_reissued_at":"2026-05-18T01:20:58.606205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:58.606205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds for Extreme Zeros of Quasi-orthogonal Ultraspherical Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kathy Driver, Martin E. Muldoon","submitted_at":"2016-01-30T00:26:42Z","abstract_excerpt":"We discuss and compare upper and lower bounds obtained by two different methods for the positive zero of the ultraspherical polynomial $C_{n}^{(\\lambda)}$ that is greater than $1$ when $-3/2 < \\lambda < -1/2.$ Our first approach uses mixed three term recurrence relations and interlacing of zeros while the second approach uses a method going back to Euler and Rayleigh and already applied to Bessel functions and Laguerre and $q$-Laguerre polynomials. We use the bounds obtained by the second method to simplify the proof of the interlacing of the zeros of $(1-x^2)C_{n}^{(\\lambda)}$ and $C_{n+1}^{("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00044","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":"1602.00044","created_at":"2026-05-18T01:20:58.606295+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.00044v2","created_at":"2026-05-18T01:20:58.606295+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00044","created_at":"2026-05-18T01:20:58.606295+00:00"},{"alias_kind":"pith_short_12","alias_value":"TNAN4Y6WBCJ6","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"TNAN4Y6WBCJ6RQXT","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"TNAN4Y6W","created_at":"2026-05-18T12:30:44.179134+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/TNAN4Y6WBCJ6RQXT7VSTSMUPHX","json":"https://pith.science/pith/TNAN4Y6WBCJ6RQXT7VSTSMUPHX.json","graph_json":"https://pith.science/api/pith-number/TNAN4Y6WBCJ6RQXT7VSTSMUPHX/graph.json","events_json":"https://pith.science/api/pith-number/TNAN4Y6WBCJ6RQXT7VSTSMUPHX/events.json","paper":"https://pith.science/paper/TNAN4Y6W"},"agent_actions":{"view_html":"https://pith.science/pith/TNAN4Y6WBCJ6RQXT7VSTSMUPHX","download_json":"https://pith.science/pith/TNAN4Y6WBCJ6RQXT7VSTSMUPHX.json","view_paper":"https://pith.science/paper/TNAN4Y6W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.00044&json=true","fetch_graph":"https://pith.science/api/pith-number/TNAN4Y6WBCJ6RQXT7VSTSMUPHX/graph.json","fetch_events":"https://pith.science/api/pith-number/TNAN4Y6WBCJ6RQXT7VSTSMUPHX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TNAN4Y6WBCJ6RQXT7VSTSMUPHX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TNAN4Y6WBCJ6RQXT7VSTSMUPHX/action/storage_attestation","attest_author":"https://pith.science/pith/TNAN4Y6WBCJ6RQXT7VSTSMUPHX/action/author_attestation","sign_citation":"https://pith.science/pith/TNAN4Y6WBCJ6RQXT7VSTSMUPHX/action/citation_signature","submit_replication":"https://pith.science/pith/TNAN4Y6WBCJ6RQXT7VSTSMUPHX/action/replication_record"}},"created_at":"2026-05-18T01:20:58.606295+00:00","updated_at":"2026-05-18T01:20:58.606295+00:00"}