Abstract:Abstract. The extremal functions f0(z) realizing the maxima of some functionals e.g. max |a3|, and max arg f (z) within the so-called universal linearly invariant family Uα (in the sense of Pommerenke [10]) have such a form that f 0 (z) looks similar to generating function for Meixner-Pollaczek (MP) polynomials [2], [8]. This fact gives motivation for the definition and study of the generalized Meixner-Pollaczek (GMP) polynomials P λ n (x; θ, ψ) of a real variable x as coefficients ofwhere the parameters λ, θ,… Show more
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