New Proofs of Some q-Series Results
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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.
KeywordsSheffer classification delta operators polynomial bases Askey-Wilson operators the q-exponential function εq
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