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

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.

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