This article is cited in 2 papers

On Polynomials Defined by the Discrete Rodrigues Formula

V. N. Sorokin<sup>ab

a</sup> Lomonosov Moscow State University
^b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow

Abstract: We study polynomials given by the discrete Rodrigues formula, which generalizes a similar formula for Meixner polynomials. Such polynomials are associated with the theory of Diophantine approximations. The saddle point method is used to find the limit distribution of zeros of scaled polynomials. An answer is received in terms of a meromorphic function on a compact Riemann surface and is interpreted using the vector equilibrium problem of the logarithmic potential theory.

Keywords: Meixner polynomial, discrete Rodrigues formula, saddle point method, algebraic function, equilibrium problem.

UDC: 517.53

MSC: 33C45

Received: 26.08.2022
Revised: 29.09.2022

DOI: 10.4213/mzm13590

 English version: Mathematical Notes, 2023, 113:3, 420–433

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