Asymptotic distribution of zeros of a certain class of hypergeometric polynomials

2013/07/18 by Addisalem Abathun, Abathun, Addisalem, Rikard Bøgvad +1 · 1 citation
Computer Science · Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Meromorphic and Entire Functions #Polynomial and algebraic computation #math.CV

paper · pdf · doi:10.48550/arxiv.1307.4991

13 pages

arxiv created 2013/07/18 · openalex publication_date 2013/07/18 · arxiv updated 2016/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the weak asymptotic behavior of the zeros of a family of a certain class of (generalized) hypergeometric polynomials, using the associated hypergeometric differential equation, as the parameters go to infinity. We describe the curve complex on which the zeros cluster, as level curves associated to integrals on an algebraic curve derived from the equation. In a certain degenerate case we make a precise conjecture, based and generalizing work by Duren, Driver et. al, and present experimental evidence for it.

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