On Asymptotics of Orthogonal Polynomials and their Q-analogues

In this project, we plan to study asymptotics of orthogonal polynomials when their degree n tends to infinity. We will investigate complex Hermite polynomials, some hypergeometric polynomials in the Askey-scheme and the corresponding q-orthogonal polynomials. The Plancherel-Rotach asymptotic expansions of these polynomials will be derived by using the difference equation method and the integral method. Important improvements of these methods will also be achieved when solving our problems.