Some 2-orthogonal polynomial eigenfunctions

Abstract

The use of a general di↵erential operator on the vectorial space of polynomial functions that does not increase the degree of polynomials [5] and its properties allowed the development of algebraic techniques for finding the corresponding polynomial eigenfunctions. We present further results of a recent symbolic approach [6] regarding di↵erential relations of third order and a specific type of multiple orthogonal polynomials, namely the 2-orthogonal polynomial sequences. These polynomial sequences are described by the corresponding fourterm recurrence relation, and its classical character is analysed.