Plancherel-Rotach asymptotics for the Charlier polynomials (Q1384648)

For the Charlier polynomials \(C_n(x,a) (x\geq 0)\) orthogonal with respect to a discrete distribution on the positive real line the asymptotics are derived. Because the asymptotics varies greatly from one region of the \(x\)-axis to another, the positive real axis is divided into the seven regions, and a corresponding asymptotic approximation for the polynomials in each of the regions are obtained.