New Characterizations of Discrete Classical Orthogonal Polynomials

✍ Scribed by K.H. Kwon; D.W. Lee; S.B. Park

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 358 KB
• Volume: 89
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1996.3028

✦ Synopsis

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 (x)] n=r are orthogonal polynomials, then [P n (x)] n=0 are classical orthogonal polynomials. We also obtain several other characterizations of discrete classical orthogonal polynomials.