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Extensions of discrete classical orthogonal polynomials beyond the orthogonality

✍ Scribed by R.S. Costas-Santos; J.F. Sánchez-Lara

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
655 KB
Volume
225
Category
Article
ISSN
0377-0427

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✦ Synopsis

It is well-known that the family of Hahn polynomials {h α,β n (x; N)} n≥0 is orthogonal with respect to a certain weight function up to degree N. In this paper we prove, by using the three-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 among them for all n ∈ N 0 . Furthermore, in order to get these results for the Krawtchouk polynomials we will obtain a more general property of orthogonality for Meixner polynomials.

📜 SIMILAR VOLUMES

New Characterizations of Discrete Classi
New Characterizations of Discrete Classical Orthogonal Polynomials
✍ K.H. Kwon; D.W. Lee; S.B. Park 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 358 KB

We prove that if both [P n (x)] n=0 and [{ r P n (x)] n=r are orthogonal polynomials for any fixed integer r 1, then [P n (x)] n=0 must be discrete classical orthogonal polynomials. This result is a discrete version of the classical Hahn's theorem stating that if both [P n (x)] n=0 and [(dÂdx) r P n