Convergence properties of discrete analogs of orthogonal polynomials
β Scribed by M. W. Wilson
- Publisher
- Springer Vienna
- Year
- 1970
- Tongue
- English
- Weight
- 191 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0010-485X
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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