{"paper":{"title":"Uniform asymptotics for discrete orthogonal polynomials on infinite nodes with an accumulation point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Shuai-Xia Xu, Xiao-Bo Wu, Yu Lin, Yu-Qiu Zhao","submitted_at":"2014-10-15T07:21:27Z","abstract_excerpt":"In this paper, we develop the Riemann-Hilbert method to study the asymptotics of discrete orthogonal polynomials on infinite nodes with an accumulation point. To illustrate our method, we consider the Tricomi-Carlitz polynomials $f_n^{(\\alpha)}(z)$ where $\\alpha$ is a positive parameter. Uniform Plancherel-Rotach type asymptotic formulas are obtained in the entire complex plane including a neighborhood of the origin, and our results agree with the ones obtained earlier in [{\\it SIAM J.\\;Math.\\;Anal} {\\bf 25} (1994)] and [{{\\it Proc.\\;Amer.\\;Math.\\;Soc.\\,}{\\bf138} (2010)}]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3948","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"}