Abbreviated Journal Title
Symmetry Integr. Geom.
Askey-Wilson polynomials; orthogonality; BIORTHOGONAL RATIONAL FUNCTIONS; CONTINUED FRACTIONS; Physics, Mathematical
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.
Symmetry Integrability and Geometry-Methods and Applications
Ismail, Mourad E.H., "Orthogonal Basic Hypergeometric Laurent Polynomials" (2012). Faculty Bibliography 2010s. 2790.