Abstract
In this Note, we study the uniform asymptotics of the Meixner–Pollaczek polynomials P n ( λ n ) ( z ; ϕ ) with varying parameter λ n = ( 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.
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