Journal article
Factorization of fourth-order differential equations for perturbed classical orthogonal polynomials
Publication Details
Authors: | Foupouagnigni, M.; Koepf, W.; Ronveaux, A. |
Publication year: | 2004 |
Journal: | Journal of Computational and Applied Mathematics |
Pages range : | 299-326 |
Volume number: | 162 |
Start page: | 299 |
End page: | 326 |
ISSN: | 0377-0427 |
Abstract
We factorize the fourth-order differential equations satisfied by the Laguerre-Hahn orthogonal polynomials obtained from some perturbations of classical orthogonal polynomials such as: the rth associated (for generic r), the general co-recursive, the general co-recursive associated, the general co-dilated and the general co-modified classical orthogonal polynomials. Moreover, we find four linearly independent solutions of the fourth-order differential equations, and show that the factorization obtained for modifications of classical orthogonal polynomials is still valid, with some minor changes when the polynomial family modified is semi-classical. Finally, we extend the validity of the results obtained for the associated classical orthogonal polynomials with integer order of association from integers to reals. (C) 2003 Elsevier B.V. All rights reserved.
We factorize the fourth-order differential equations satisfied by the Laguerre-Hahn orthogonal polynomials obtained from some perturbations of classical orthogonal polynomials such as: the rth associated (for generic r), the general co-recursive, the general co-recursive associated, the general co-dilated and the general co-modified classical orthogonal polynomials. Moreover, we find four linearly independent solutions of the fourth-order differential equations, and show that the factorization obtained for modifications of classical orthogonal polynomials is still valid, with some minor changes when the polynomial family modified is semi-classical. Finally, we extend the validity of the results obtained for the associated classical orthogonal polynomials with integer order of association from integers to reals. (C) 2003 Elsevier B.V. All rights reserved.
