Uniform asymptotic expansions for Charlier polynomials (Q5958889)

The author investigates the asymptotic behavior of the Charlier polynomials \(C_n^{(a)}\) as \(n \to \infty \). The polynomials \(C_n^{(a)}\) are not regarded as functions of \(x\) with \(a\) as a parameter, but rather with the roles reversed via a second-order linear differential equation in which \(a\) is the (real or complex valued) independent variable and \(x\) is a parameter.