ASYMPTOTICS OF THE ASSOCIATED POLLACZEK POLYNOMIALS

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Author(s)

  • Min-Jie Luo
  • R. Wong

Detail(s)

Original languageEnglish
Pages (from-to)2583-2597
Journal / PublicationProceedings of the American Mathematical Society
Volume147
Issue number6
Online published20 Feb 2019
Publication statusPublished - Jun 2019

Abstract

In this note, we investigate the large-n behavior of the associated Pollaczek polynomials P nλ ( z; a, b, c ). These polynomials involve four real parameters λ, a, b, and c, in addition to the complex variable z. Asymptotic formulas are derived for these polynomials, when z lies in the complex plane bounded away from the interval of orthogonality (-1,1), as well as in the interior of the interval of orthogonality. In the process of studying the asymptotic behavior of these polynomials when z ∈ C \ [−1, 1], we found that the existing representations of P nλ ( z; a, b, c ) do not provide useful information about their large-n asymptotics. Here, we present a new representation in terms of the Gauss hypergeometric functions, from which the large-n asymptotics for z in C \ [-1, 1] can be readily obtained. The asymptotic approximation in the interior of the interval of orthogonality is obtained by using asymptotic theory for difference equations.

Research Area(s)

  • Asymptotics, difference equations, hypergeometric functions, Pollaczek polynomials, SIEVED ORTHOGONAL POLYNOMIALS

Citation Format(s)

ASYMPTOTICS OF THE ASSOCIATED POLLACZEK POLYNOMIALS. / Luo, Min-Jie; Wong, R.
In: Proceedings of the American Mathematical Society, Vol. 147, No. 6, 06.2019, p. 2583-2597.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review