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On -symmetric classical -orthogonal polynomials

✍ Scribed by Y. Ben Cheikh; N. Ben Romdhane

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
235 KB
Volume
236
Category
Article
ISSN
0377-0427

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✦ Synopsis

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 applications, we characterize the d-symmetric classical d-orthogonal polynomials of Boas-Buck type, we construct a (d + 1)-order linear differential equation with polynomial coefficients satisfied by each polynomial of a d-symmetric classical d-orthogonal set and we show that the d-symmetric classical d-orthogonal property is preserved by the derivative operator. Some of the obtained properties appear to be new, even for the case d = 1.

πŸ“œ SIMILAR VOLUMES

New Characterizations of Discrete Classi
New Characterizations of Discrete Classical Orthogonal Polynomials
✍ K.H. Kwon; D.W. Lee; S.B. Park πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 358 KB

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 [(dΓ‚dx) r P n