Volume 27, pp. 113-123, 2007.
Orthogonal polynomials and recurrence equations, operator equations and factorization
Wolfram Koepf
Abstract
This article surveys the classical orthogonal polynomial systems
of the Hahn class, which are solutions of second-order
differential, difference or -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.
Full Text (PDF) [206 KB],
BibTeX
Key words
orthogonal polynomials, Hahn class, differential equations, difference equations, -difference equations, hypergeometric functions, factorization of operator polynomials, computer algebra, Maple
AMS subject classifications
33C45, 33C20, 33D45, 33D15, 39A70
