## Abstract

The Askey-Wilson polynomials are orthogonal polynomials in x = cos θ, which are given as a terminating 4φ3 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 4φ3's. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single 4φ3'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.

Original language | English (US) |
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Article number | 092 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

Volume | 8 |

DOIs | |

State | Published - 2012 |

## Keywords

- Askey-wilson polynomials
- Orthogonality