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

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.


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Last updated on 2019-25-07 at 11:24