q-Ultraspherical polynomials for q a root of unity

Details q-Ultraspherical polynomials for q a root of unity q-Ultraspherical polynomials for q a root of unity

1996-05-21

arxiv.org/abs/q-alg/9605033v1

Lett. Math. Phys. 37 (1996) 173-180

Mathematics

Quantum Algebra

7 pages, LATEX

Scientific paper

10.1007/BF00416020

Properties of the $q$-ultraspherical polynomials for $q$ being a primitive
root of unity are derived using a formalism of the $so_q(3)$ 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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