Extensions of discrete classical orthogonal polynomials beyond the orthogonality

Date: 2007..11..02
Event: Mathematics Department Colloquium
Venue: Mathematics Department Colloquium. College of William and Mary, USA

Abstract

It is well-known that the family of Hahn polynomials is orthogonal with respect to certain weight function up to degree N. In this talk we prove, by using the tree-term recurrence relation which this family satisfies, that the Hahn polynomials can be characterized by a ∆-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 between them for all positive integer n. 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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