Extensions of discrete classical orthogonal polynomials beyond the orthogonality
Copyright policy )Extensions of discrete classical orthogonal polynomials beyond the orthogonality
It is well known that the family of Hahn polynomials $\{h_n^{��,��}(x;N)\}_{n\ge 0}$ 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 $��$-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.
2 figures, 20 pages
- Universidad Loyola Andalucía Spain
- Universidad Politécnica de Madrid Spain
- University of California, San Francisco United States
- University of California System United States
- University of California, Santa Barbara United States
Computational Mathematics, Mathematics - Classical Analysis and ODEs, Applied Mathematics, Classical orthogonal polynomials, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Inner product involving difference operators, Non-standard orthogonality, 33C45, 26C05
Computational Mathematics, Mathematics - Classical Analysis and ODEs, Applied Mathematics, Classical orthogonal polynomials, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Inner product involving difference operators, Non-standard orthogonality, 33C45, 26C05
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