Aufsatz in einer Fachzeitschrift
Orthogonal polynomials and recurrence equations, operator equations and factorization
Details zur Publikation
Autor(inn)en: | Koepf, W. |
Publikationsjahr: | 2007 |
Zeitschrift: | Electronic Transactions on Numerical Analysis |
Seitenbereich: | 113-123 |
Jahrgang/Band : | 27 |
Erste Seite: | 113 |
Letzte Seite: | 123 |
ISSN: | 1068-9613 |
URN / URL: |
Zusammenfassung, 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.
