scholarly journals Uniform Asymptotics for Discrete Orthogonal Polynomials with Respect to Varying Exponential Weights on a Regular Infinite Lattice

2010 ◽  
Author(s):  
P. Bleher ◽  
K. Liechty
Keyword(s):  
Orthogonal Polynomials ◽  
Uniform Asymptotics ◽  
Exponential Weights ◽  
Infinite Lattice ◽  
Discrete Orthogonal Polynomials ◽  
Discrete Orthogonal

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

2016 ◽  
Vol 14 (05) ◽  
pp. 705-737 ◽  
Author(s):  
Xiao-Bo Wu ◽  
Yu Lin ◽  
Shuai-Xia Xu ◽  
Yu-Qiu Zhao
Keyword(s):  
Orthogonal Polynomials ◽  
Asymptotic Expansions ◽  
Accumulation Point ◽  
Asymptotic Formulas ◽  
Positive Parameter ◽  
Uniform Asymptotics ◽  
Discrete Orthogonal Polynomials ◽  
Entire Complex ◽  
Discrete Orthogonal ◽  
Uniform Asymptotic Expansions

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 [Formula: see text] where [Formula: see text] 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 [W. M. Y. Goh and J. Wimp, On the asymptotics of the Tricomi–Carlitz polynomials and their zero distribution. I, SIAM J. Math. Anal. 25 (1994) 420–428] and in [K. F. Lee and R. Wong, Uniform asymptotic expansions of the Tricomi–Carlitz polynomials, Proc. Amer. Math. Soc. 138 (2010) 2513–2519].

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