Sieved ultraspherical polynomials
In mathematics, the two families cλ
n(x;k) and Bλ
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
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