q-Ultraspherical polynomials for q a root of unity
V. Spiridonov, A. Zhedanov
Abstract
Properties of the q-ultraspherical polynomials for q being a primitive root of unity are derived using a formalism of the soq(3) algebra. The orthogonality condition for these polynomials provides a new class of trigonometric identities representing discrete finite-dimensional analogs of q-beta integrals of Ramanujan.
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