A characterization of classical orthogonal Laurent polynomials
β Scribed by E. Hendriksen
- Book ID
- 108495301
- Publisher
- Elsevier Science
- Year
- 1988
- Weight
- 588 KB
- Volume
- 91
- Category
- Article
- ISSN
- 1385-7258
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π SIMILAR VOLUMES
Let [h n (z)] be the sequence of polynomials, satisfying where \* n # [0, 2n], n # N. For a wide class of weights d\(x) and under the assumption lim n Γ \* n Γ(2n)=% # [0, 1], two descriptions of the zero asymptotics of [h n (z)] are obtained. Furthermore, their analogues for polynomials orthogonal
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