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Another Characterization of the Classical Orthogonal Polynomials

✍ 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
DOI: 10.1137/0503007

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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