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.
Categories: math.CA math.CV