Asymptotics for some $q$-hypergeometric polynomials

TL;DR

This paper investigates the local asymptotic behavior of certain $q$-hypergeometric polynomials, providing insights into their zero distributions and illustrating findings with numerical examples.

Contribution

It introduces new Mehler--Heine asymptotics for specific $q$-hypergeometric polynomials, advancing understanding of their zero behavior.

Findings

Derived Mehler--Heine asymptotics for selected $q$-hypergeometric polynomials

Analyzed the asymptotic distribution of zeros of these polynomials

Provided numerical illustrations supporting theoretical results

Abstract

We tackle the study of a type of local asymptotics, known as Mehler--Heine asymptotics, for some $q$--hypergeometric polynomials. Some consequences about the asymptotic behavior of the zeros of these polynomials are discussed. We illustrate the results with numerical examples.