Journal article
Orthogonal polynomials and recurrence equations, operator equations and factorization
Publication Details
Authors: | Koepf, W. |
Publication year: | 2007 |
Journal: | Electronic Transactions on Numerical Analysis |
Pages range : | 113-123 |
Volume number: | 27 |
Start page: | 113 |
End page: | 123 |
ISSN: | 1068-9613 |
URN / URL: |
Abstract
This article surveys the classical orthogonal polynomial systems of the Hahn class, which are solutions of second-order differential, difference or q-difference equations. Orthogonal families satisfy three-term recurrence equations. Example applications of an algorithm to determine whether a three-term recurrence equation has solutions in the Hahn class-implemented in the computer algebra system Maple-are given. Modifications of these families, in particular associated orthogonal systems, satisfy fourth-order operator equations. A factorization of these equations leads to a solution basis.
This article surveys the classical orthogonal polynomial systems of the Hahn class, which are solutions of second-order differential, difference or q-difference equations. Orthogonal families satisfy three-term recurrence equations. Example applications of an algorithm to determine whether a three-term recurrence equation has solutions in the Hahn class-implemented in the computer algebra system Maple-are given. Modifications of these families, in particular associated orthogonal systems, satisfy fourth-order operator equations. A factorization of these equations leads to a solution basis.