Uniform asymptotics for Meixner-Pollaczek polynomials with varying parameters

摘要

In this Note, we study the uniform asymptotics of the Meixner-Pollaczek polynomials P_n~((λn))(z;φ) with varying parameter λn=(n+1/2)A as n→ ∞, where A>. 0 is a constant. Uniform asymptotic expansions in terms of parabolic cylinder functions and elementary functions are obtained for z in two overlapping regions which together cover the whole complex plane.