Mehler-Heine type formulas for Charlier and Meixner polynomials

TL;DR

This paper derives asymptotic formulas for Charlier and Meixner polynomials, providing insights into their behavior near zero and the distribution of their zeros as degree increases.

Contribution

It introduces Mehler-Heine type asymptotic formulas for these polynomials and their associated families, enhancing understanding of their asymptotic behavior.

Findings

Asymptotic formulas valid near x=0

Determination of zero distribution as degree grows

Approximate behavior of polynomials in the neighborhood of zero

Abstract

We derive Mehler--Heine type asymptotic formulas for Charlier and Meixner polynomials, and also for their associated families. These formulas provide good approximations for the polynomials in the neighborhood of $x=0,$ and determine the asymptotic limit of their zeros as the degree $n$ goes to infinity.