An electrostatic model for the roots of discrete classical orthogonal polynomials

Abstract

An electrostatic model is presented to describe the behaviour of the roots of classical discrete orthogonal polynomials. Indeed, this model applies in the more general frame of polynomial solutions of second-order linear difference equations $$AΔ_h\nabla_h y+BΔ_h y+ C y=0\,,$$ where $A$, $B$ and $C$ are polynomials and $$Δ_h f(x)=f(x+h)-f(x)\qquad \text{ and }\qquad \nabla_h f(x)=f(x)-f(x-h)$$ with $h>0$.