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arXiv · 1410.3948

Uniform asymptotics for discrete orthogonal polynomials on infinite nodes with an accumulation point

Xiao-Bo Wu·Yu Lin·Shuai-Xia Xu·Yu-Qiu Zhao
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Abstract

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 $f_n^{(α)}(z)$ where $α$ 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)}].

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Xiao-Bo Wu, Yu Lin, Shuai-Xia Xu, Yu-Qiu Zhao. 2014-10-15. Uniform asymptotics for discrete orthogonal polynomials on infinite nodes with an accumulation point. https://arxiv.org/abs/1410.3948

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