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

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

1996-05-21

arxiv.org/abs/q-alg/9605034v2

Duke Math. J. 89 (1997), 283--305

Mathematics

Quantum Algebra

18 pages, LATEX

Scientific paper

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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