Semi-classical linear functionals and integral representation II

Abstract

In this article, we give a new family of linear functionals u p , which proves that the list of integral representation given by Belmehdi [Belmehdi, S. (1992). On semi-classical linear functionals of class s = 1. Classification and integral representations. Indagationes Mathematicae, New Series 3(3), 262, (4.9)–(4.11)] is not complete. The recurrence coefficients as well as the differential equations of u 2, u 3 and u 4 are explicitly given.