Extensions of discrete classical orthogonal polynomials beyond the orthogonality

Abstract

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.

2 figures, 20 pages

References in corpus (2)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports

Cited by in corpus (6)

• On Polynomials Orthogonal with Respect to an Inner Product Involving Higher-Order Differences: The Meixner Case
• A new approach to the asymptotics for Sobolev orthogonal polynomials
• A Survey on q-Polynomials and their Orthogonality Properties
• The power collection method for connection relations: Meixner polynomials
• The Laguerre constellation of classical orthogonal Polynomials
• Zeros of Meixner and Krawtchouk polynomials