In this talk, we will present uniform and non-uniform asymptotics of the Charlier polynomials by using difference equation methods alone. The Charlier polynomials are special in that they do not fit into the framework of the turning point theory, despite the fact that they are crucial in the Askey scheme. Asymptotic approximations are obtained respectively in the outside region, an intermediate region, and near the turning points.  In particular, we obtain uniform asymptotic approximation at a pair of coalescing turning points with the aid of a local transformation. This is joint work with Xiaomin Huang and Yuqiu Zhao.

海报