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Extensions of discrete classical orthogonal polynomials beyond the orthogonality
Costas-Santos, R. S. Sanchez-Lara, J. F.
Costas-Santos, R. S.
Sanchez-Lara, J. F.
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.
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2009-01-01
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Mathematics
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10.1016/j.cam.2008.07.055