Semi-classical Linear Functionals of Class Four: The Symmetric Case

Abstract

In this paper, we obtain all the symmetric semi-classical linear functionals of class four taking into account the irreducible expression of the corresponding Pearson equation. We focus our attention on their integral representations. Thus, some linear functionals very well known in the literature, associated with perturbations of semi-classical linear functionals of class two at most, appear as well as new linear functionals which have not been studied.