Asymptotics for Multiple Meixner Polynomials

TL;DR

This paper investigates the asymptotic properties of Multiple Meixner polynomials, employing algebraic functions and equilibrium problems to describe zero distributions and analyze recurrence coefficients.

Contribution

It introduces a novel algebraic function approach to derive the asymptotics and zero distribution of Multiple Meixner polynomials.

Findings

Zero distribution characterized by equilibrium measures

Main asymptotic term derived from recurrence coefficients

Method applicable to first and second kind polynomials

Abstract

We study the asymptotic behavior of Multiple Meixner polynomials of first and second kind, respectively (see J. Arves\'u et al. J. Comput. Appl. Math., 153, (2003)). We use an algebraic function formulation for the solution of the equilibrium problem with constrain to describe their zero distribution. Then analyzing the limiting behavior of the coefficients of the recurrence relations for Multiple Meixner polynomials we obtain the main term of their asymptotics.