Journal article

Orthogonal polynomials and recurrence equations, operator equations and factorization

Publication Details

Journal: | Electronic Transactions on Numerical Analysis |

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.