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SIGMA, 2012, Volume 8, 092, 20 pages (Mi sigma769)  

This article is cited in 1 scientific paper (total in 1 paper)

Orthogonal Basic Hypergeometric Laurent Polynomials

Mourad E. H. Ismailab, Dennis Stantonc

a Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA
b Department of Mathematics, King Saud University, Riyadh, Saudi Arabia
c School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA

Abstract: The Askey–Wilson polynomials are orthogonal polynomials in $x = \cos \theta$, which are given as a terminating $_4\phi_3$ basic hypergeometric series. The non-symmetric Askey–Wilson polynomials are Laurent polynomials in $z=e^{i\theta}$, which are given as a sum of two terminating $_4\phi_3$'s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single $_4\phi_3$'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.

Keywords: Askey–Wilson polynomials; orthogonality

DOI: https://doi.org/10.3842/SIGMA.2012.092

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Full text: http://emis.mi.ras.ru/.../092
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MSC: 33D45
Received: August 4, 2012; in final form November 28, 2012; Published online December 1, 2012
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Citation: Mourad E. H. Ismail, Dennis Stanton, “Orthogonal Basic Hypergeometric Laurent Polynomials”, SIGMA, 8 (2012), 092, 20 pp.

Citation in format AMSBIB
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\by Mourad~E.~H.~Ismail, Dennis~Stanton
\paper Orthogonal Basic Hypergeometric Laurent Polynomials
\jour SIGMA
\yr 2012
\vol 8
\papernumber 092
\totalpages 20
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    This publication is cited in the following articles:
    1. Ismail M.E.H., Simeonov P., “Heine Representations and Monotonicity Properties of Determinants and Pfaffians”, Constr. Approx., 41:2 (2015), 231–249  crossref  mathscinet  zmath  isi  elib  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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