{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4JCNPB7ENNI7GWXBH5MN4EHCZG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"648d9338dbcd5b3e7839c921076ea6770bce27dd7fd867091c8fd6eafbb11c17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-08T05:55:17Z","title_canon_sha256":"87bdcb759bd3bf87120803e548694ea0097bc731d35cbbe9f6b21e97184498b9"},"schema_version":"1.0","source":{"id":"1202.1606","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1606","created_at":"2026-05-18T03:33:26Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1606v3","created_at":"2026-05-18T03:33:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1606","created_at":"2026-05-18T03:33:26Z"},{"alias_kind":"pith_short_12","alias_value":"4JCNPB7ENNI7","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4JCNPB7ENNI7GWXB","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4JCNPB7E","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:8f647e0e02a4e43a71d8645652545a1ae4ca4bb55474887bfd1efcfeaf7e5180","target":"graph","created_at":"2026-05-18T03:33:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider two positive, normalized measures dA(x) and dB(x) related by the relationship dA(x)=(C/(x+D))dB(x) or by dA(x) = (C/(x^2+E))dB(x) and dB(x) is symmetric. We show that then the polynomial sequences {a_{n}(x)}, {b_{n}(x)} orthogonal with respect to these measures are related by the relationship a_{n}(x)=b_{n}(x)+{\\kappa}_{n}b_{n-1}(x) or by a_{n}(x) = b_{n}(x) + {\\lambda}_{n}b_{n-2}(x) for some sequences {{\\kappa}_{n}} and {{\\lambda}_{n}}. We present several examples illustrating this fact and also present some attempts for extensions and generalizations. We also give some universal ","authors_text":"Pawe{\\l} J. Szab{\\l}owski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-08T05:55:17Z","title":"On affinity relating two positive measures and the connection coefficients between polynomials orthogonalized by these measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1606","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1f65399b0bb983ce1a6e3563aa4623b09070e18e143db480e0a480b059422f0b","target":"record","created_at":"2026-05-18T03:33:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"648d9338dbcd5b3e7839c921076ea6770bce27dd7fd867091c8fd6eafbb11c17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-08T05:55:17Z","title_canon_sha256":"87bdcb759bd3bf87120803e548694ea0097bc731d35cbbe9f6b21e97184498b9"},"schema_version":"1.0","source":{"id":"1202.1606","kind":"arxiv","version":3}},"canonical_sha256":"e244d787e46b51f35ae13f58de10e2c9a5920cda6b0f27bda27d7519dcd4145e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e244d787e46b51f35ae13f58de10e2c9a5920cda6b0f27bda27d7519dcd4145e","first_computed_at":"2026-05-18T03:33:26.323897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:26.323897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NvkV1VMhzq1TnVY0nywoBEuwR/XWXg4ypfVV9OlKyny56cu2wQlU5KcJAVSbUoB7Pu8ot3dLdiec0GFfvI8hBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:26.324629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.1606","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f65399b0bb983ce1a6e3563aa4623b09070e18e143db480e0a480b059422f0b","sha256:8f647e0e02a4e43a71d8645652545a1ae4ca4bb55474887bfd1efcfeaf7e5180"],"state_sha256":"ef398fca548b80d3eba0435d70a32cf99a8e87c6875c5cac4ac302a0a78026c0"}