{"paper":{"title":"An inequality for Jacobi polynomials of form $P_n^{(\\alpha_n,\\beta_n)}(x)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Yuyuan Ouyang, Zhulin He","submitted_at":"2017-04-21T02:42:42Z","abstract_excerpt":"We prove an inequality for Jacobi polynomials that \\begin{align} \\Delta_n(x):=P_n^{(\\alpha_n,\\beta_n)}(x)P_n^{(\\alpha_{n+1},\\beta_{n+1})}(x)- P_{n-1}^{(\\alpha_n,\\beta_n)}(x)P_{n+1}^{(\\alpha_{n+1},\\beta_{n+1})}(x)\\le 0,\\ \\forall x\\ge 1, \\end{align} where $\\alpha_n=an$ and $\\beta_n=bn$ for some $a,b\\ge 0$. The above inequality has a similar taste as the Tu\\'ran type inequalities, but with $\\alpha_n$ and $\\beta_n$ that depends linearly on $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06381","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":""},"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"}