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arXiv · 1212.0077

Orthogonal Basic Hypergeometric Laurent Polynomials

Mourad E. H. Ismail·Dennis Stanton
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Abstract

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.

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BibTeXRIS

Mourad E. H. Ismail, Dennis Stanton. 2012-12-01. Orthogonal Basic Hypergeometric Laurent Polynomials. https://doi.org/10.3842/sigma.2012.092

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