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q-Ultraspherical polynomials for q a root of unity |
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| Authors: | Vyacheslav Spiridonov Alexei Zhedanov |
| Affiliation: | (1) Centre de Recherches Mathématiques, Université de Montréal, Succ. Centre-ville, C.P. 6128, H3C 3J7 Montréal, Québec, Canada;(2) Physics Department, Donetsk University, 340055 Donetsk, Ukraine;(3) Present address: Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia |
| 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 analogues of q-beta integrals of Ramanujan. |
| Keywords: | 17B37 33D80 |
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