Uniform asymptotics for the discrete Laguerre polynomials

In this paper, we consider the discrete Laguerre polynomials [Formula: see text] orthogonal with respect to weight function supported on infinite nodes text]. We focus “band-saturated region” situation when parameter As text], uniform expansions for are achieved in different regions complex plane. Typically, Airy-function and Gamma-function derived near endpoints of band origin, respectively. The asymptotics normalizing coefficient recurrence coefficients also obtained. Our method is based Deift–Zhou steepest descent Riemann–Hilbert problems.