Discrete-time Volterra chain and classical orthogonal polynomials
β Scribed by Spiridonov, Vyacheslav; Zhedanov, Alexei
- Book ID
- 125501797
- Publisher
- Institute of Physics
- Year
- 1997
- Tongue
- English
- Weight
- 153 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0305-4470
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π SIMILAR VOLUMES
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 [(dΓdx) r P n
It is well-known that the family of Hahn polynomials {h Ξ±,Ξ² n (x; N)} nβ₯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 β-Sob