Global Asymptotics of the Meixner Polynomials
Classical Analysis and ODEs
2015-03-17 v1
Abstract
Using the steepest descent method for oscillatory Riemann-Hilbert problems introduced by Deift and Zhou [Ann. Math. {\bf 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 on the positive real line by using the steepest descent method for integrals [Constr. Approx. {\bf 14}(1998), 113-150].
Keywords
Cite
@article{arxiv.1101.4370,
title = {Global Asymptotics of the Meixner Polynomials},
author = {X. -S. Wang and R. Wong},
journal= {arXiv preprint arXiv:1101.4370},
year = {2015}
}