Zeros and orthogonality of the Askey-Wilson polynomials for q a root of unityReportar como inadecuado



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


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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.



Autor: V. Spiridonov; A. Zhedanov

Fuente: https://archive.org/







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