Title Extensions of discrete classical orthogonal polynomials beyond the orthogonality
Authors COSTAS SANTOS, ROBERTO SANTIAGO, Sanchez-Lara, J. F.
External publication Si
Means J. Comput. Appl. Math.
Scope Article
Nature Científica
JCR Quartile 1
SJR Quartile 2
JCR Impact 1.29200
SJR Impact 0.81000
Web https://www.scopus.com/inward/record.uri?eid=2-s2.0-58849128184&doi=10.1016%2fj.cam.2008.07.055&partnerID=40&md5=01df80a00de326a12f3e2129521ec9c4
Publication date 15/03/2009
ISI 000263986100012
Scopus Id 2-s2.0-58849128184
DOI 10.1016/j.cam.2008.07.055
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.\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.
Keywords Classical orthogonal polynomials; Inner product involving difference operators; Non-standard orthogonality
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