On a General Family of 2-Orthogonal Polynomial Eigenfunctions of a Third Order Differential Equation via Symbolic Computation

The search for 2-orthogonal polynomial eigenfunctions, with respect to a third order differential operator that does not increase the degree of polynomials, was recently developed in [23] by means of a symbolic approach. This work allowed us to establish some impossible cases as also to present a few families of such 2-orthogonal polynomial sequences. In this paper, we apply the symbolic setup proposed in [23] in order to enlighten us about further 2-orthogonal polynomial solutions of this problem. Concerning a general family inhere described, it is also proved its Hahn-classical character. Additionally, some functional identities are established.