Differential Relations of Functionals Associated with 2-Orthogonal Eigenfunctions

Considering a differential operator of third order that does not increase the degree of polynomials, we establish some properties of the dual sequence of the corresponding 2-orthogonal polynomial eigenfunctions. Taking into account the symbolic approach developed in a recent work [18] which enabled us to issue some new 2-orthogonal sequences, we developed the analogous approach in the dual space. The identities fulfilled by the main forms allow us to analyse Hahn’s property, that is to say, identify if the sequence of derivatives is also a 2-orthogonal polynomial sequence.