Authors

M. E. H. Ismail;D. Stanton

Comments

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Abbreviated Journal Title

Symmetry Integr. Geom.

Keywords

Askey-Wilson polynomials; orthogonality; BIORTHOGONAL RATIONAL FUNCTIONS; CONTINUED FRACTIONS; Physics, Mathematical

Abstract

The Askey-Wilson polynomials are orthogonal polynomials in x = cos theta, which are given as a terminating (4)phi(3) basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in z = e(i theta), which are given as a sum of two terminating (4)phi(3)'s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single (4)phi(3)'s which are Laurent polynomials in z are given, which imply the non-symmetric Askey-Wilson biorthogonality. These results include discrete orthogonality relations. They can be considered as a classical analytic study of the results for non-symmetric Askey-Wilson polynomials which were previously obtained by affine Hecke algebra techniques.

Journal Title

Symmetry Integrability and Geometry-Methods and Applications

Volume

8

Publication Date

1-1-2012

Document Type

Article

Language

English

First Page

20

WOS Identifier

WOS:000312436200001

ISSN

1815-0659

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