2-Orthogonal polynomials and Darboux transformations. Applications to the discrete Hahn-classical case. Issue 3 (4th March 2021) - Marcellán, F.; Chaggara, H.; Ayadi, N.
Abstract : In this paper, we are interested in the following problem. We assume that P n n ≥ 0 is a monic 2-orthogonal polynomial sequence and we analyse the existence of a sequence of 2-orthogonal polynomials Q n n ≥ 0 such that we have a decomposition P n ( x ) = Q n ( x ) + a n Q n − 1 ( x ), a n ≠ 0, n ≥ 1. This constitutes the counterpart in the framework of 2-orthogonality of those associated with the Christoffel transformation in the standard case. Some illustrative examples are shown.