Orthogonal basic hypergeometric Laurent polynomials

Mourad E.H. Ismail, Dennis Stanton

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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, 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 languageEnglish (US)
Article number092
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
StatePublished - 2012


  • Askey-wilson polynomials
  • Orthogonality

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