Orthogonal Basic Hypergeometric Laurent Polynomials

The Askey-Wilson polynomials are orthogonal polynomials in $x = \cos θ$, which are given as a terminating $_4ϕ_3$ basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in $z=e^{iθ}$, which are given as a sum of two terminating $_4ϕ_3$'s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single $_4ϕ_3$'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.

No reviews yet.

No comments yet.