On an extension of symmetric coherent pairs of orthogonal polynomials

Given two symmetric and positive definite linear functionals, W and V, we study the coefficients in the recurrence relation for the system of monic polynomials orthogonal with respect to the second linear functional assuming that the first one is classical and that there exists an algebraic-differential relation between these two families of polynomials. Moreover, we determine this companion linear functional as a rational modification of the classical one.