Global Asymptotics of the Hahn Polynomials
Classical Analysis and ODEs
2012-10-09 v1 Complex Variables
Abstract
In this paper, we study the asymptotics of the Hahn polynomials Q_n(x; {\alpha}, {\beta}, N) as the degree n grows to infinity, when the parameters {\alpha} and {\beta} are fixed and the ratio of n/N = c is a constant in the interval (0, 1). Uniform asymptotic formulas in terms of Airy functions and elementary functions are obtained for z in three overlapping regions, which together cover the whole complex plane. Our method is based on a modified version of the Riemann-Hilbert approach introduced by Deift and Zhou.
Keywords
Cite
@article{arxiv.1210.2359,
title = {Global Asymptotics of the Hahn Polynomials},
author = {Y. Lin and R. Wong},
journal= {arXiv preprint arXiv:1210.2359},
year = {2012}
}
Comments
44 pages, 7 figures