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# Paper: Extensions of discrete classical orthogonal polynomials beyond the orthogonality

 ELSEVIER SCIENCE BV (NETHERLANDS) | ISSN: 0377-0427 | JCR® 2009 Impact Factor: 1.292 - MATHEMATICS, APPLIED — position: 46/204 (Q1/T1) title

## Extensions of discrete classical orthogonal polynomials beyond the orthogonality

Costas-Santos, R. S. and Sanchez-Lara, J. F. Journal of Computational and Applied Mathematics 225, no. 2 (2009), 440 — 451

## Abstract

It is well-known that the family of Hahn polynomials 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 $$n\in \mathbb N$$. Furthermore, in order to get these results for the Krawtchouk polynomials we will obtain a more general property of orthogonality for Meixner polynomials.

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## BibTeX

@article {MR2494714,
AUTHOR = {Costas-Santos, R. S.; Sanchez-Lara, J. F.},
TITLE = {Extensions of discrete classical orthogonal polynomials beyond the orthogonality},
JOURNAL = {J. Comput. Appl. Math.},
FJOURNAL = {Journal of Computational and Applied Mathematics},
VOLUME = {225},
NUMBER={2},
YEAR = {2009},
PAGES = {440--451},
ISSN = {1081-3810},
MRCLASS = {33C45 (33C47 42C05)},
MRNUMBER = {MR2494714},
ZBL = {1167.42008},
MRREVIEWER = {Alicia Cachafeiro},
DOI = {10.1016/j.cam.2008.07.055},
URL = {https://doi.org/10.1016/j.cam.2008.07.055},
}