Extensions of discrete classical orthogonal polynomials beyond the orthogonality

Details Extensions of discrete classical orthogonal polynomials beyond the orthogonality Extensions of discrete classical orthogonal polynomials beyond the orthogonality

2007-10-25

arxiv.org/abs/0710.4930v5

J. Comp. Appl. Math. 225 (2009) pp. 440-451

Mathematics

Classical Analysis and ODEs

2 figures, 20 pages

Scientific paper

10.1016/j.cam.2008.07.055

It is well known that the family of Hahn polynomials $\{h_n^{\alpha,\beta}(x;N)\}_{n\ge 0}$ is orthogonal with respect to a certain weight function up to $N$. In this paper we present a factorization for Hahn polynomials for a degree higher than $N$ and we prove that these polynomials can be characterized by a $\Delta$-Sobolev orthogonality. We also present an analogous result for dual-Hahn, Krawtchouk, and Racah polynomials and give the limit relations between them for all $n\in \XX N_0$. Furthermore, in order to get this results for the Krawtchouk polynomials we will get a more general property of orthogonality for Meixner polynomials.

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