Fourth-order difference equation for the associated classical discrete orthogonal polynomials

Abstract

We derive the fourth-order difference equation satisfied by the associated order r of classical orthogonal polynomials of a discrete variable. The coefficients of this equation are given in terms of the polynomials φ and τ which appear in the discrete Pearson equation Δ( φϱ) = τϱ defining the weight ϱ( x) of the classical discrete orthogonal polynomials.