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

Authors:
M. Foupouagnigni;A. Ronveaux
Affiliations:
Département de Mathématiques, Ecole Normale Supérieure, Université de Yaoundé I, BP 47, Yaoundé, Cameroon;Mathematical Physics, Facultés Universitaires Notre-Dame de la Paix, B-5000 Namur, Belgium
Venue:
Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
Year:
2003

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Abstract

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.