Global asymptotics of the Meixner polynomials

Article type: Research Article

Authors: Wang, X.-S.^; | Wong, R.

Affiliations: Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

Note: [] Corresponding author. E-mail: xswang4@mail.ustc.edu.cn.

Abstract: Using the steepest descent method for oscillatory Riemann–Hilbert problems introduced by Deift and Zhou [Ann. Math. 137 (1993), 295–368], we derive asymptotic formulas for the Meixner polynomials in two regions of the complex plane separated by the boundary of a rectangle. The asymptotic formula on the boundary of the rectangle is obtained by taking limits from either inside or outside. Our results agree with the ones obtained earlier for z on the positive real line by using the steepest descent method for integrals [Constr. Approx. 14 (1998), 113–150].

Keywords: global asymptotics, Meixner polynomials, Riemann–Hilbert problems, Airy function

DOI: 10.3233/ASY-2011-1060

Journal: Asymptotic Analysis, vol. 75, no. 3-4, pp. 211-231, 2011