# Sieved ultraspherical polynomials

In mathematics, the two families *c*^{λ}_{n}(*x*;*k*) and *B*^{λ}_{n}(*x*;*k*) of **sieved ultraspherical polynomials**, introduced by Waleed Al-Salam, W.R. Allaway and Richard Askey in 1984, are the archetypal examples of sieved orthogonal polynomials. Their recurrence relations are a modified (or "sieved") version of the recurrence relations for ultraspherical polynomials.

## Recurrence relations

For the sieved ultraspherical polynomials of the first kind the recurrence relations are

- if
*n*is not divisible by*k*

For the sieved ultraspherical polynomials of the second kind the recurrence relations are

- if
*n*is not divisible by*k*

## References

- Al-Salam, Waleed; Allaway, W. R.; Askey, Richard (1984), "Sieved ultraspherical polynomials",
*Transactions of the American Mathematical Society*,**284**(1): 39–55, doi:10.2307/1999273, ISSN 0002-9947, JSTOR 1999273, MR 0742411

This article is issued from
Wikipedia.
The text is licensed under Creative
Commons - Attribution - Sharealike.
Additional terms may apply for the media files.