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Zeros and orthogonality of the Askey-Wilson polynomials for q a root of unity

V. Spiridonov·A. Zhedanov
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Abstract

We study some properties of the Askey-Wilson polynomials (AWP) when q is a primitive N-th root of unity. For general four-parameter AWP, zeros of the N-th polynomial and the orthogonality measure are found explicitly. Special subclasses of the AWP, e.g., the continuous q-Jacobi and big q-Jacobi polynomials, are considered in detail. A set of discrete weight functions positive on a real interval is described. Some new trigonometric identities related to the AWP are obtained. Normalization conditions of some polynomials are expressed in terms of the Gauss sums.

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BibTeXRIS

V. Spiridonov, A. Zhedanov. 2005-11-18. Zeros and orthogonality of the Askey-Wilson polynomials for q a root of unity. https://arxiv.org/abs/q-alg/9605034

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