Document Type
Article
Department/Program
Mathematics
Journal Title
Journal of Computational and Applied Mathematics
Pub Date
2009
Volume
225
Issue
2
First Page
440
Abstract
It is well-known that the family of Hahn polynomials {h(n)(alpha,beta) (x; N)}(n >= 0) is orthogonal with respect to a certain weight function up to degree N. In this paper we prove, by using the three-term recurrence relation which this family satisfies, that the Hahn polynomials can be characterized by a Delta-Sobolev orthogonality for every n and present a factorization for Hahn polynomials for a degree higher than N. We also present analogous results for dual Hahn, Krawtchouk, and Racah polynomials and give the limit relations among them for all n is an element of N(0). Furthermore, in order to get these results for the Krawtchouk polynomials we will obtain a more general property of orthogonality for Meixner polynomials. (c) 2008 Elsevier B.V. All rights reserved.
Recommended Citation
Costas-Santos, R. S. and Sanchez-Lara, J. F., Extensions of discrete classical orthogonal polynomials beyond the orthogonality (2009). Journal of Computational and Applied Mathematics, 225(2), 440-451.
10.1016/j.cam.2008.07.055
DOI
10.1016/j.cam.2008.07.055
