Properties of the zeros of the polynomials belonging to the Askey scheme

TL;DR

This paper investigates the zeros of Askey scheme polynomials, revealing new properties and Diophantine relations under specific parameter restrictions, advancing understanding of their algebraic structure.

Contribution

It introduces novel properties and Diophantine relations of zeros for Askey scheme polynomials, expanding theoretical knowledge in this area.

Findings

New properties of zeros identified

Diophantine relations established for zeros

Parameter restrictions lead to specific zero relations

Abstract

In this paper we provide properties---which are, to the best of our knowledge, new---of the zeros of the polynomials belonging to the Askey scheme. These findings include Diophantine relations satisfied by these zeros when the parameters characterizing these polynomials are appropriately restricted.