Difference equations for the co-recursive rth associated orthogonal polynomials of the Dq-Laguerre–Hahn class

摘要

We use some relations between the rth associated orthogonal polynomials of the Dq-Laguerre–Hahn class to derive the fourth-order q-difference equation satisfied by the co-recursive rth associated orthogonal polynomials of the Dq-Laguerre–Hahn class.When r=1 and for q-semi-classical situations, this q-difference equation factorizes as product of two second-order q-difference equations. Finally, we study some classical situations, and give some examples relative to the co-recursive associated discrete q-Hermite II orthogonal polynomials.