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Plancherel-Rotach asymptotics for the Charlier polynomials. (English) Zbl 0894.33004
For the Charlier polynomials C n (x,a)(x0) 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.
MSC:
33C45Orthogonal polynomials and functions of hypergeometric type