From Wikipedia, the free encyclopedia
This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources. Find sources: "Sieved orthogonal polynomials" – news · newspapers · books · scholar · JSTOR (May 2024) |
This article includes inline citations, but they are not properly formatted. Please improve this article by correcting them. (May 2024) (Learn how and when to remove this message) |
In mathematics, sieved orthogonal polynomials are orthogonal polynomials whose recurrence relations are formed by sieving the recurrence relations of another family; in other words, some of the recurrence relations are replaced by simpler ones. The first examples were the sieved ultraspherical polynomials introduced by Waleed Al-Salam, W. R. Allaway, and Richard Askey (1984). Mourad Ismail later studied sieved orthogonal polynomials in a long series of papers. Other families of sieved orthogonal polynomials that have been studied include sieved Pollaczek polynomials, and sieved Jacobi polynomials.
References
[edit]- Al-Salam, Waleed; Allaway, W. R.; Askey, Richard (1984), "Sieved ultraspherical polynomials", Transactions of the American Mathematical Society, 284 (1): 39–55, CiteSeerX 10.1.1.308.3668, doi:10.2307/1999273, ISSN 0002-9947, JSTOR 1999273, MR 0742411
This polynomial-related article is a stub. You can help Wikipedia by expanding it. |
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url
url