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q-Ultraspherical polynomials for q a root of unity

V. Spiridonov·A. Zhedanov
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Abstract

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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BibTeXRIS

V. Spiridonov, A. Zhedanov. 1996-05-21. q-Ultraspherical polynomials for q a root of unity. https://doi.org/10.1007/bf00416020

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