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
Classical symmetric orthogonal polynomials of a discrete variable
✍ Scribed by Area, I.; Godoy†, E.; Ronveaux‡, A.; Zarzo§, A.
- Book ID
- 118208476
- Publisher
- Taylor and Francis Group
- Year
- 2004
- Tongue
- English
- Weight
- 134 KB
- Volume
- 15
- Category
- Article
- ISSN
- 1065-2469
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📜 SIMILAR VOLUMES
A general theory of classical orthogonal polynomials of a discrete variable on nonuniform lattices is developed. The classification of the polynomials under consideration is given.
The d-symmetric classical d-orthogonal polynomials are an extension of the standard symmetric classical polynomials according to the Hahn property. In this work, we give some characteristic properties for these polynomials related to generating functions and recurrence-differential equations. As app
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