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

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.

References in corpus (5)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Superintegrability in two dimensions and the Racah-Wilson algebra
• Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials
• On the Equilibrium Configuration of the BC-type Ruijsenaars-Schneider System
• Properties of the zeros of the polynomials belonging to the Askey scheme

Cited by in corpus (7)

• Properties of the zeros of the polynomials belonging to the Askey scheme
• Perturbations around the zeros of classical orthogonal polynomials
• Finite-dimensional representations of difference operators, and the identification of remarkable matrices
• Solutions of convex Bethe Ansatz equations and the zeros of (basic) hypergeometric orthogonal polynomials
• Stable equilibria for the roots of the symmetric continuous Hahn and Wilson polynomials
• Solvable dynamical systems and isospectral matrices defined in terms of the zeros of orthogonal or otherwise special polynomials
• Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials