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- Title
GLOBAL ASYMPTOTICS OF THE HAHN POLYNOMIALS.
- Authors
LIN, Y.; WONG, R.
- Abstract
In this paper, we study the asymptotics of the Hahn polynomials Qn(x; α, (β, N) as the degree n grows to infinity, when the parameters a and β 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.
- Subjects
GLOBAL asymptotic stability; HAHN-Banach theorem; POLYNOMIALS; AIRY functions; RIEMANN-Roch theorems; MATHEMATICAL analysis
- Publication
Analysis & Applications, 2013, Vol 11, Issue 3, p1
- ISSN
0219-5305
- Publication type
Article
- DOI
10.1142/S0219530513500188