Sieved ultraspherical polynomials

In mathematics, the two families "c"("x";"k") and "B"("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
For the sieved ultraspherical polynomials of the second kind the recurrence relations are