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We give necessary and sufficient conditions under which a conjecture by Askey, that the zeros of Jacobi polynomials $P_n^{(\\alpha, \\beta)}$ and $P_{n}^{(\\alpha,\\beta+2)}$ are interlacing, holds when the parameters $\\alpha$ and $\\beta$ are in the range $\\alpha>-1$ and $-2<\\beta<-1$. We prove that the zeros of $P_n^{(\\alpha, \\beta)}$ and $P_{n+1}^{(\\alpha,\\beta)}$ do not interlace for any $n\\in\\mathbb{N}$, $n\\geq2$ and any fixed $\\alpha$, $\\be"},"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":"1510.08599","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.CA","submitted_at":"2015-10-29T08:34:57Z","cross_cats_sorted":[],"title_canon_sha256":"a4fad0c14516995bd16a139957ae84a38d450b409d3593353f5ef7be85df431c","abstract_canon_sha256":"dff7e058bc0ca66074b2cc4645f08ab717e52d1ba61bd256b49fc127f0a96dd1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:09.569893Z","signature_b64":"91vevxfRhM0t5+YS3VWqdUEOHg8/n/Hmmxov4PHaDYHEoxrkF/yOoZ5h1NOyTY2LMmrtxLYjx5vwO5I40o9rDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0272f073b20b1cb0ded88e3933dd9b4f06091230c44d5a69baf45c9ce56bb759","last_reissued_at":"2026-05-18T01:16:09.569284Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:09.569284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Zeros of Quasi-Orthogonal Jacobi Polynomials","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kathy Driver, Kerstin Jordaan","submitted_at":"2015-10-29T08:34:57Z","abstract_excerpt":"We consider interlacing properties satisfied by the zeros of Jacobi polynomials in quasi-orthogonal sequences characterised by $\\alpha>-1$, $-2<\\beta<-1$. We give necessary and sufficient conditions under which a conjecture by Askey, that the zeros of Jacobi polynomials $P_n^{(\\alpha, \\beta)}$ and $P_{n}^{(\\alpha,\\beta+2)}$ are interlacing, holds when the parameters $\\alpha$ and $\\beta$ are in the range $\\alpha>-1$ and $-2<\\beta<-1$. 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