Orthogonal Basic Hypergeometric Laurent Polynomials

Symmetry, Integrability and Geometry: Methods and Applications

关键词: Askey-Wilson polynomials;    orthogonality;   

DOI  :  

来源: DOAJ

【 摘 要 】

The Askey-Wilson polynomials are orthogonal polynomials in$x = cos heta$, which are given as a terminating $_4phi_3$ basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in $z=e^{iheta}$, which are given as a sum of two terminating $_4phi_3$'s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single$_4phi_3$'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-symmetricAskey-Wilson polynomials which were previously obtained by affine Hecke algebra techniques.

【 授权许可】

Unknown