Global Asymptotics for Meixner-Pollaczek Polynomials with a Varying Parameter

Authors


Address for correspondence: R. Wong, Department of Mathematics, City University of Hong Kong, Hong Kong; e-mail: mawong@cityu.edu.hk

Abstract

In this paper, we study the uniform asymptotics of the Meixner-Pollaczek polynomials math formula with varying parameter math formula as math formula, where A > 0 is a constant. Two asymptotic expansions are obtained, which hold uniformly for z in two overlapping regions which together cover the whole complex plane. One involves parabolic cylinder functions, and the other is in terms of elementary functions only. Our approach is based on the steepest descent method for oscillatory Riemann-Hilbert problems first introduced by Deift and Zhou [1].

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