Discrete orthogonal polynomials – polynomial modification of a classical functional
✍ Scribed by Ronveaux, A.; Salto, L.
- Book ID
- 121364569
- Publisher
- Taylor and Francis Group
- Year
- 2001
- Tongue
- English
- Weight
- 554 KB
- Volume
- 7
- Category
- Article
- ISSN
- 1023-6198
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📜 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 [(dÂdx) r P n
Based on the general theory, we consider the continuous orthogonality property for classical polynomials of a discrete variable on nonuniform lattices. ## I. Introduction. Preliminary Notions and Notations Classical orthogonal polynomials (Jacobi, Laguerre and Hermite) are the simplest solutions