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The famous Hilbert matrix is included as a particular case. The direct sum $B(a,b,c)\\oplus B(a+1,b+1,c)$ is shown to commute with a discrete analog of the dilatation operator. It follows that there exists a three-parameter family of real symmetric Jacobi m"},"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":"1506.01064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-02T21:14:57Z","cross_cats_sorted":[],"title_canon_sha256":"0d7f8f399d0a8fab85a25f53dd255d65b2ead0c68bb708ca45d0d4bc90678b55","abstract_canon_sha256":"5d6d984cb95f72b0812fcc5fd0a76726d8d38ddbce7a169dfc1f318e85dad1cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:59.583406Z","signature_b64":"xIPTizOtnSlgVKwLuNPX5lJ8pGF05EbN7ycGM1R2rfwA3Lz2GULCjWUIDF4GKoTUVM53YuyPVcAHu4pRwhovAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9f29614192d405bfecb1115db481b0e535c4434adadda2b1266191f8aab9400","last_reissued_at":"2026-05-18T01:35:59.582761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:59.582761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Family of explicitly diagonalizable weighted Hankel matrices generalizing the Hilbert matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Pavel Stovicek, Tomas Kalvoda","submitted_at":"2015-06-02T21:14:57Z","abstract_excerpt":"A three-parameter family $B=B(a,b,c)$ of weighted Hankel matrices is introduced with the entries \\[ B_{j,k}=\\frac{\\Gamma(j+k+a)}{\\Gamma(j+k+b+c)}\\,\\sqrt{\\frac{\\Gamma(j+b)\\Gamma(j+c)\\Gamma(k+b)\\Gamma(k+c)}{\\Gamma(j+a)\\, j!\\,\\Gamma(k+a)\\, k!}}\\,, \\] $j,k\\in\\mathbb{Z}_{+}$, supposing $a$, $b$, $c$ are positive and $a<b+c$, $b<a+c$, $c\\leq a+b$. The famous Hilbert matrix is included as a particular case. The direct sum $B(a,b,c)\\oplus B(a+1,b+1,c)$ is shown to commute with a discrete analog of the dilatation operator. 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