Extensions of discrete classical orthogonal polynomials beyond the orthogonality
نویسنده
چکیده
It is well known that the family of Hahn polynomials {hα,β n (x;N)}n≥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 ∈ N0. 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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تاریخ انتشار 2007