Sieved ultraspherical polynomials

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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[edit]

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[edit]