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Moreover, the polynomial sequences $$\\biggl\\{\\sum_{k=0}^n\\JS(n,k;z)y^k\\biggr\\}_{n\\geq 0}\\quad \\text{and} \\quad \\biggl\\{\\sum_{k=0}^n\\js(n,k;z)y^k\\biggr\\}_{n\\geq 0}$$ are proved to be strongly $\\{z,y\\}$-log-convex. In the same vein, we extend a recent result of Chen et al. about the Ramanujan polynomials to Chapoton's generaliz"},"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":"1309.4237","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-17T09:13:04Z","cross_cats_sorted":[],"title_canon_sha256":"504f53a91d0eaee319f2d6fb30b46d17d1d535480cffa0c94943441a1d6e4637","abstract_canon_sha256":"80547c64a4c2b0099c59b58ac8e285c7790b831d95d07e1b096c8942cba44fb9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:13.985931Z","signature_b64":"GKJ16S3UaftAVPUoxEMW8vz9aSZUWGOWl7x9vFHQV6m9kYcR9NXyhqHYG4SuXBOTCV2tl0VTOOhNEyltmRmWDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a9f84ca2c358a9082bb784974ab40cbce6807ca8fc8812dea95cf5d0e0c524a","last_reissued_at":"2026-05-18T03:10:13.985404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:13.985404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Positivity properties of Jacobi-Stirling numbers and generalized Ramanujan polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jiang Zeng, Zhicong Lin","submitted_at":"2013-09-17T09:13:04Z","abstract_excerpt":"Generalizing recent results of Egge and Mongelli, we show that each diagonal sequence of the Jacobi-Stirling numbers $\\js(n,k;z)$ and $\\JS(n,k;z)$ is a P\\'olya frequency sequence if and only if $z\\in [-1, 1]$ and study the $z$-total positivity properties of these numbers. Moreover, the polynomial sequences $$\\biggl\\{\\sum_{k=0}^n\\JS(n,k;z)y^k\\biggr\\}_{n\\geq 0}\\quad \\text{and} \\quad \\biggl\\{\\sum_{k=0}^n\\js(n,k;z)y^k\\biggr\\}_{n\\geq 0}$$ are proved to be strongly $\\{z,y\\}$-log-convex. 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