On the asymptotics of the Meixner-Pollaczek polynomials and their zeros

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Original languageEnglish
Pages (from-to)59-90
Journal / PublicationConstructive Approximation
Issue number1
Publication statusPublished - 2001


An infinite asymptotic expansion is derived for the Meixner-Pollaczek polynomials Mn (nα; δ, η) as n → ∞, which holds uniformly for -M ≤ α ≤ M, where M can be any positive number. This expansion involves the parabolic cylinder function and its derivative. If αn,s denotes the sth zero of Mn(nα; δ, η), counted from the right, and if α̃n,s denotes its sth zero counted from the left, then for each fixed s, three-term asymptotic approximations are obtained for both αn,s and α̃n,s as n → ∞.

Research Area(s)

  • Meixner-Pollaczek polynomials, Parabolic cylinder functions, Uniform asymptotic expansions, Zeros