Characterizations of Bochner–Krall Orthogonal Polynomials of Jacobi Type
✍ Scribed by K.H. Kwon; D.W. Lee
- Book ID
- 106045587
- Publisher
- Springer
- Year
- 2003
- Tongue
- English
- Weight
- 207 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0176-4276
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📜 SIMILAR VOLUMES
Let {Sn}n denote a sequence of polynomials orthogonal with respect to the Sobolev inner product where ¿ 0 and {d 0; d 1} is a so-called coherent pair with at least one of the measures d 0 or d 1 a Jacobi measure. We investigate the asymptotic behaviour of Sn(x), for n → +∞ and x ÿxed, x ∈ C \ [ -1;
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