This article is cited in 3 papers

A generalization of the discrete Rodrigues formula for Meixner polynomials

V. N. Sorokin

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: A generalization of Meixner polynomials leading to a new construction of Apéry approximations is put forward. The limiting distribution of the zeros of scaled polynomials is described in terms of algebraic functions. The resulting distribution is shown to be a solution of some vector equilibrium problem in the theory of logarithmic potential.
Bibliography: 21 titles.

Keywords: Meixner polynomials, discrete Rodrigues formula, Apéry approximations, saddle-point method, algebraic functions, equilibrium problem.

MSC: 42C05

Received: 30.03.2022 and 19.07.2022

DOI: 10.4213/sm9765

 English version: Sbornik: Mathematics, 2022, 213:11, 1559–1581

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