{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:KHPULOWKDUC5GM5CE63Z6U2FYX","short_pith_number":"pith:KHPULOWK","schema_version":"1.0","canonical_sha256":"51df45baca1d05d333a227b79f5345c5f7bb9a1c003b9a1ccd5e8e89f2a70534","source":{"kind":"arxiv","id":"2011.00255","version":1},"attestation_state":"computed","paper":{"title":"On difference equations of Kravchuk-Sobolev type polynomials of higher order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Anier Soria-Lorente, Roberto S. Costas-Santos","submitted_at":"2020-10-31T12:08:24Z","abstract_excerpt":"In this contribution we consider sequences of monic polynomials orthogonal with respect to Sobolev-type inner product \\[ \\left\\langle f,g\\right\\rangle _{\\lambda,\\mu}\\!=\\!\\sum_{x=0}^Nf(x)g(x)\\frac{\\Gamma(N+1) p^x(1-p)^{N-x} }{\\Gamma (N-x+1) \\Gamma(x+1) }+\\lambda\\Delta^j f(0)\\Delta^j g(0)+\\mu\\Delta^j f(N)\\Delta^j g(N), \\] where $0<p <1$, $\\lambda,\\mu\\in \\mathbb R_{+}$, $n\\leq N\\in \\mathbb Z_{+}$, $j\\in \\mathbb Z_{+}$ and $\\Delta$ denotes the forward difference operators. We derive an explicit representation for these polynomials. In addition, the ladder operators associated with these polynomial"},"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":"2011.00255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-10-31T12:08:24Z","cross_cats_sorted":[],"title_canon_sha256":"5ce1d919af185456ff5ce619dac7ac9fdcef5addf17a05407f1e08b17b78b2fc","abstract_canon_sha256":"abe6b8f6af4ddf3b83d3adef3162914ab0fd56c65d0893912434a42c991ec097"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:47:58.943598Z","signature_b64":"xod/hSGaAgmTe4LtTtQ2sLIurATNpcUOnJLYwEdGmwd4AEM7C4EENrl8cO24DcLK7YSGZKWXTdgSFOLKnCHRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51df45baca1d05d333a227b79f5345c5f7bb9a1c003b9a1ccd5e8e89f2a70534","last_reissued_at":"2026-07-05T01:47:58.943193Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:47:58.943193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On difference equations of Kravchuk-Sobolev type polynomials of higher order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Anier Soria-Lorente, Roberto S. Costas-Santos","submitted_at":"2020-10-31T12:08:24Z","abstract_excerpt":"In this contribution we consider sequences of monic polynomials orthogonal with respect to Sobolev-type inner product \\[ \\left\\langle f,g\\right\\rangle _{\\lambda,\\mu}\\!=\\!\\sum_{x=0}^Nf(x)g(x)\\frac{\\Gamma(N+1) p^x(1-p)^{N-x} }{\\Gamma (N-x+1) \\Gamma(x+1) }+\\lambda\\Delta^j f(0)\\Delta^j g(0)+\\mu\\Delta^j f(N)\\Delta^j g(N), \\] where $0<p <1$, $\\lambda,\\mu\\in \\mathbb R_{+}$, $n\\leq N\\in \\mathbb Z_{+}$, $j\\in \\mathbb Z_{+}$ and $\\Delta$ denotes the forward difference operators. We derive an explicit representation for these polynomials. In addition, the ladder operators associated with these polynomial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.00255","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.00255/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2011.00255","created_at":"2026-07-05T01:47:58.943247+00:00"},{"alias_kind":"arxiv_version","alias_value":"2011.00255v1","created_at":"2026-07-05T01:47:58.943247+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.00255","created_at":"2026-07-05T01:47:58.943247+00:00"},{"alias_kind":"pith_short_12","alias_value":"KHPULOWKDUC5","created_at":"2026-07-05T01:47:58.943247+00:00"},{"alias_kind":"pith_short_16","alias_value":"KHPULOWKDUC5GM5C","created_at":"2026-07-05T01:47:58.943247+00:00"},{"alias_kind":"pith_short_8","alias_value":"KHPULOWK","created_at":"2026-07-05T01:47:58.943247+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.07429","citing_title":"From Thought to Action: How a Hierarchy of Neural Dynamics Supports Language Production","ref_index":29,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KHPULOWKDUC5GM5CE63Z6U2FYX","json":"https://pith.science/pith/KHPULOWKDUC5GM5CE63Z6U2FYX.json","graph_json":"https://pith.science/api/pith-number/KHPULOWKDUC5GM5CE63Z6U2FYX/graph.json","events_json":"https://pith.science/api/pith-number/KHPULOWKDUC5GM5CE63Z6U2FYX/events.json","paper":"https://pith.science/paper/KHPULOWK"},"agent_actions":{"view_html":"https://pith.science/pith/KHPULOWKDUC5GM5CE63Z6U2FYX","download_json":"https://pith.science/pith/KHPULOWKDUC5GM5CE63Z6U2FYX.json","view_paper":"https://pith.science/paper/KHPULOWK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2011.00255&json=true","fetch_graph":"https://pith.science/api/pith-number/KHPULOWKDUC5GM5CE63Z6U2FYX/graph.json","fetch_events":"https://pith.science/api/pith-number/KHPULOWKDUC5GM5CE63Z6U2FYX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KHPULOWKDUC5GM5CE63Z6U2FYX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KHPULOWKDUC5GM5CE63Z6U2FYX/action/storage_attestation","attest_author":"https://pith.science/pith/KHPULOWKDUC5GM5CE63Z6U2FYX/action/author_attestation","sign_citation":"https://pith.science/pith/KHPULOWKDUC5GM5CE63Z6U2FYX/action/citation_signature","submit_replication":"https://pith.science/pith/KHPULOWKDUC5GM5CE63Z6U2FYX/action/replication_record"}},"created_at":"2026-07-05T01:47:58.943247+00:00","updated_at":"2026-07-05T01:47:58.943247+00:00"}