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Another Characterization of the Classical Orthogonal Polynomials

โœ Scribed by Al-Salam, W. A.; Chihara, T. S.


Book ID
118198493
Publisher
Society for Industrial and Applied Mathematics
Year
1972
Tongue
English
Weight
427 KB
Volume
3
Category
Article
ISSN
0036-1410

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New Characterizations of Discrete Classi
โœ K.H. Kwon; D.W. Lee; S.B. Park ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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 [(dร‚dx) r P n