In this talk, we consider a sequence of orthogonal polynomials introduced by Meixner in 1934 and Pollaczek in 1949. These polynomials play an important role in quantum systems, random matrix theory, and representation theory. We aim to derive the asymptotic approximations for these polynomials as the degree grows to infinity. The primary tool is the asymptotic theory for linear difference equations established by Z. Wang, X.-S. Wang and R. Wong. In the classical case, i.e., when the associated parameter c=0, our results coincide with the previous results by the integral approach in X. Li and R. Wong (Constructive Approximations, 2001, 59-90). This is a joint work with Wen-Gao Long.

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