Fourth order q-difference equation for the first associated of the q-classical orthogonal polynomials

摘要

We derive the fourth-order q-difference equation satisfied by the first associated of the q-classical orthogonal polynomials. The coefficients of this equation are given in terms of the polynomials σ and τ which appear in the q-Pearson difference equation Dq(σ ϱ) = τϱ defining the weight ϱ of the q-classical orthogonal polynomials inside the q-Hahn tableau.