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.