The electrostatic equilibrium problem for classical discrete orthogonal polynomials

Abstract

We present two types of generic difference characterizations of zeros of the classical discrete orthogonal polynomials associated with a discrete weight function satisfying a difference equation of the Pearson type. These characterizations use either the total forward or modified partial central difference operators of discrete discriminants, which approximate the total electrostatic energy of the system of n n unit charges moving freely on an interval in presence of external potential given by the iterated discrete weight.