Asymptotic distribution of the zeros of a certain family of generalized hypergeometric polynomials

Abstract

The primary aim of this paper is to investigate the asymptotic distribution of the zeros of certain classes of hypergeometric polynomials. We employ classical analytical techniques, including Watson's lemma and the method of steepest descent, to understand the asymptotic behavior of these polynomials: q + 1 F q ( − n , k n + α , … , k n + α + q − 1 q ; k n + β , … , k n + β + q − 1 q ; z ) ( n → ∞ ) , where n is a nonnegative integer, q is a positive integer and the constant parameters α and β are constrained by . By applying the general results established in this paper, we generate numerical evidence and graphical illustrations using Mathematica to show the clustering of zeros on certain curves.