In this paper, we consider a perturbation of a Laguerre–Hahn functional by adding a derivative of a Dirac delta. This transformation leaves invariant the family of Laguerre–Hahn linear functionals. We shall also analyse the class of the perturbed linear functional. Finally, we illustrate these perturbations by adding the derivative of a Dirac delta to the first kind associated functional of the classical Laguerre functional. The expression of the new orthogonal polynomials is obtained.
