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 [(dΓdx) r P n
β¦ LIBER β¦
Dual equations and classical orthogonal polynomials
β Scribed by Richard Askey
- Publisher
- Elsevier Science
- Year
- 1968
- Tongue
- English
- Weight
- 405 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0022-247X
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In 1929, S. Bochner identified the families of polynomials which are eigenfunctions of a second-order linear differential operator. What is the appropriate generalization of this result to bivariate polynomials? One approach, due to Krall and Sheffer in 1967 and pursued by others, is to determine wh