New Proofs of Some q-Series Results

  • Mourad E.H. Ismail
  • Ruiming Zhang
Part of the Developments in Mathematics book series (DEVM, volume 13)


We use a Sheffer classification technique to give very short proofs of the addition theorem for the ε q function, the representation of ε q as a multiple of a 2ϕ1, and a relatively new representation of ε q . A direct proof of the evaluation of the connection coefficients of the Askey-Wilson polynomials and the Nassrallah-Rahman integral are also given. A sim ple proof of a characterization theorem for the continuous q-Hermite polynomials is also given.


Sheffer classification delta operators polynomial bases Askey-Wilson operators the q-exponential function εq 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Mourad E.H. Ismail
    • 1
  • Ruiming Zhang
    • 2
  1. 1.Department of MathematicsUniversity of Central FloridaOrlando
  2. 2.Department of MathematicsUniversity of South FloridaTampa

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