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When $a=-N$, $N\\in\\nn$ and $t=\\frac1{p}$, the polynomials $K_n(x;p,N)=(-N)_n\\phantom{}_2F_1(-n,-x;-N;\\frac1{p})$, $n=0,1,...N$, $0<p<1$ are referred to as Krawtchouk polynomials. We prove results for the zero location of the orthogonal polynomials $K_{n}(x;p,a)$, $0<p<1$ and $a>n-1$, the quasi-orthogonal polynomials $K_{n}(x;p,a)$, $k-1<a<k$, $k=1,...,n-1$ and $p>1$ or $p<0$ as well as the non-orthogonal pol"},"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":"0901.0817","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-01-07T13:07:12Z","cross_cats_sorted":[],"title_canon_sha256":"6104a28fa9f85e035cbb77c1c54105e6fe3cb570cf28b4c78d4e940c630a2c10","abstract_canon_sha256":"2735f41e765a4b8c1e976751440d04fdeb038c551537c5f196439aa009268f7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:39.037870Z","signature_b64":"ZQYMm3RYip2Rc/xVS6O5ZWYy9pu5a9F43DbNdlSjqC2MJ6Cbq5szl6TJqdtFxSmasWQW9L4hwdIvR96OrXx7BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d58392860bd688115e85e190e47289acd0f4ee72ae9f298bfd6c8d341cd4fe8f","last_reissued_at":"2026-05-18T04:20:39.037110Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:39.037110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Zeros of Meixner and Krawtchouk polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A Jooste, F Tookos, K Jordaan","submitted_at":"2009-01-07T13:07:12Z","abstract_excerpt":"We investigate the zeros of a family of hypergeometric polynomials $_2F_1(-n,-x;a;t)$, $n\\in\\nn$ that are known as the Meixner polynomials for certain values of the parameters $a$ and $t$. When $a=-N$, $N\\in\\nn$ and $t=\\frac1{p}$, the polynomials $K_n(x;p,N)=(-N)_n\\phantom{}_2F_1(-n,-x;-N;\\frac1{p})$, $n=0,1,...N$, $0<p<1$ are referred to as Krawtchouk polynomials. We prove results for the zero location of the orthogonal polynomials $K_{n}(x;p,a)$, $0<p<1$ and $a>n-1$, the quasi-orthogonal polynomials $K_{n}(x;p,a)$, $k-1<a<k$, $k=1,...,n-1$ and $p>1$ or $p<0$ as well as the non-orthogonal pol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0817","kind":"arxiv","version":3},"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":"0901.0817","created_at":"2026-05-18T04:20:39.037233+00:00"},{"alias_kind":"arxiv_version","alias_value":"0901.0817v3","created_at":"2026-05-18T04:20:39.037233+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.0817","created_at":"2026-05-18T04:20:39.037233+00:00"},{"alias_kind":"pith_short_12","alias_value":"2WBZFBQL22EB","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"2WBZFBQL22EBCXUF","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"2WBZFBQL","created_at":"2026-05-18T12:25:58.018023+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/2WBZFBQL22EBCXUF4GIOI4UJVT","json":"https://pith.science/pith/2WBZFBQL22EBCXUF4GIOI4UJVT.json","graph_json":"https://pith.science/api/pith-number/2WBZFBQL22EBCXUF4GIOI4UJVT/graph.json","events_json":"https://pith.science/api/pith-number/2WBZFBQL22EBCXUF4GIOI4UJVT/events.json","paper":"https://pith.science/paper/2WBZFBQL"},"agent_actions":{"view_html":"https://pith.science/pith/2WBZFBQL22EBCXUF4GIOI4UJVT","download_json":"https://pith.science/pith/2WBZFBQL22EBCXUF4GIOI4UJVT.json","view_paper":"https://pith.science/paper/2WBZFBQL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0901.0817&json=true","fetch_graph":"https://pith.science/api/pith-number/2WBZFBQL22EBCXUF4GIOI4UJVT/graph.json","fetch_events":"https://pith.science/api/pith-number/2WBZFBQL22EBCXUF4GIOI4UJVT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2WBZFBQL22EBCXUF4GIOI4UJVT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2WBZFBQL22EBCXUF4GIOI4UJVT/action/storage_attestation","attest_author":"https://pith.science/pith/2WBZFBQL22EBCXUF4GIOI4UJVT/action/author_attestation","sign_citation":"https://pith.science/pith/2WBZFBQL22EBCXUF4GIOI4UJVT/action/citation_signature","submit_replication":"https://pith.science/pith/2WBZFBQL22EBCXUF4GIOI4UJVT/action/replication_record"}},"created_at":"2026-05-18T04:20:39.037233+00:00","updated_at":"2026-05-18T04:20:39.037233+00:00"}