COSTAS SANTOS, ROBERTO SANTIAGO, Sanchez-Lara, J. F.
Si
J. Comput. Appl. Math.
Article
Científica
1.292
0.81
15/03/2009
000263986100012
2-s2.0-58849128184
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.
Classical orthogonal polynomials; Inner product involving difference operators; Non-standard orthogonality