Jump to content

Sieved orthogonal polynomials

From Wikipedia, the free encyclopedia

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