Uniform asymptotics for Meixner-Pollaczek polynomials with varying parameters (Q643608)

From the authors' abstract: The authors study the uniform asymptotics of the Meixner-Pollaczek polynomials \(P^\lambda_n (z;\phi)\) with varying parameter \(\lambda_n = (n+\frac 12)A\) as \(n\to \infty \), 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.