Abstract
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.
Research partially supported by NSF grant DMS 99-70865. This work was done at the University of South Florida
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Ismail, M.E., Zhang, R. (2005). New Proofs of Some q-Series Results. In: Ismail, M.E., Koelink, E. (eds) Theory and Applications of Special Functions. Developments in Mathematics, vol 13. Springer, Boston, MA. https://doi.org/10.1007/0-387-24233-3_12
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DOI: https://doi.org/10.1007/0-387-24233-3_12
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