2-Orthogonal polynomials and Darboux transformations. Applications to the discrete Hahn-classical case. Issue 3 (4th March 2021)

• Record Type: Journal Article
• Authors: Marcellán, F.; Chaggara, H.; Ayadi, N.
• Is Part Of: Journal of difference equations and applications. Volume 27:Issue 3(2021)
• Page Start: 431
• Page End: 452
• Publication Date: 2021-03-04
• Subjects: 2-orthogonal polynomials -- Darboux transformation -- discrete Hahn-classical polynomials; 33C45 -- 39A70 -- 41A10 -- 41A58; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2021.1905804
• Languages: English
• ISSNs: 1023-6198

Abstract

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.