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In this paper, we study the asymptotic behavior as $n\\to \\infty$ of the Shannon entropy $\\mathcal S ((\\Psi_n(x))= -\\sum_{j=1}^n \\Psi_{n,j}(x) \\log (\\Psi_{n,j}(x))$, $x\\in (-1,1)$, when the orthogonality weight is $ (1-x)^{\\alpha}\\, (1+x)^{\\beta}\\, h(x) $, $\\alpha, \\beta > -1$, and where $"},"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":"1410.2286","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-10-08T21:26:48Z","cross_cats_sorted":[],"title_canon_sha256":"8b19ddf6d2300eb7dfd01878ba23ea16c223e237aff8c3705d14550856205d10","abstract_canon_sha256":"9e15b04f56d9d8f8fa3cfd0623ee4937cf46e0ce5573d7e128bfdc0968b80f1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:58.343886Z","signature_b64":"B+9bu4qGk/EBJWV9LAaZht6l8MN2I4zgcHiSIG7lTfIYF8gI9pDCfXzy45y79maW3Nt0r1Fbod05XfEY0HkwAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed346c56cf98f115b447f08f1fcc0b5209f29c4d67d5329a8a1257cc86020937","last_reissued_at":"2026-05-18T01:59:58.343219Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:58.343219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discrete Entropy of Generalized Jacobi Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ana Pe\\~na, Andrei Martinez-Finkelshtein, Paul Nevai","submitted_at":"2014-10-08T21:26:48Z","abstract_excerpt":"Given a sequence of orthonormal polynomials on $\\Bbb R$,$\\{p_n\\}_{n\\geq 0}$, with $p_n$ of degree $n$, we define the discrete probability distribution $\\Psi_n(x) = \\left(\\Psi_{n,1}(x), \\dots \\Psi_{n,n}(x) \\right) $, with $\\Psi_{n,j}(x) = \\big(\\sum_{j=0}^{n-1} p_j^2(x)\\big)^{-1} p_{j-1}^2(x)$, $j=1, \\dots, n$. In this paper, we study the asymptotic behavior as $n\\to \\infty$ of the Shannon entropy $\\mathcal S ((\\Psi_n(x))= -\\sum_{j=1}^n \\Psi_{n,j}(x) \\log (\\Psi_{n,j}(x))$, $x\\in (-1,1)$, when the orthogonality weight is $ (1-x)^{\\alpha}\\, (1+x)^{\\beta}\\, h(x) $, $\\alpha, \\beta > -1$, and where $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2286","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":"1410.2286","created_at":"2026-05-18T01:59:58.343324+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.2286v2","created_at":"2026-05-18T01:59:58.343324+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2286","created_at":"2026-05-18T01:59:58.343324+00:00"},{"alias_kind":"pith_short_12","alias_value":"5U2GYVWPTDYR","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"5U2GYVWPTDYRLNCH","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"5U2GYVWP","created_at":"2026-05-18T12:28:16.859392+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/5U2GYVWPTDYRLNCH6CHR7TALKI","json":"https://pith.science/pith/5U2GYVWPTDYRLNCH6CHR7TALKI.json","graph_json":"https://pith.science/api/pith-number/5U2GYVWPTDYRLNCH6CHR7TALKI/graph.json","events_json":"https://pith.science/api/pith-number/5U2GYVWPTDYRLNCH6CHR7TALKI/events.json","paper":"https://pith.science/paper/5U2GYVWP"},"agent_actions":{"view_html":"https://pith.science/pith/5U2GYVWPTDYRLNCH6CHR7TALKI","download_json":"https://pith.science/pith/5U2GYVWPTDYRLNCH6CHR7TALKI.json","view_paper":"https://pith.science/paper/5U2GYVWP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.2286&json=true","fetch_graph":"https://pith.science/api/pith-number/5U2GYVWPTDYRLNCH6CHR7TALKI/graph.json","fetch_events":"https://pith.science/api/pith-number/5U2GYVWPTDYRLNCH6CHR7TALKI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5U2GYVWPTDYRLNCH6CHR7TALKI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5U2GYVWPTDYRLNCH6CHR7TALKI/action/storage_attestation","attest_author":"https://pith.science/pith/5U2GYVWPTDYRLNCH6CHR7TALKI/action/author_attestation","sign_citation":"https://pith.science/pith/5U2GYVWPTDYRLNCH6CHR7TALKI/action/citation_signature","submit_replication":"https://pith.science/pith/5U2GYVWPTDYRLNCH6CHR7TALKI/action/replication_record"}},"created_at":"2026-05-18T01:59:58.343324+00:00","updated_at":"2026-05-18T01:59:58.343324+00:00"}