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An Operator Calculus for the Askey-Wilson Operator
Mourad E.H.Ismail
Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700, USA
ismail@math.usf.edu
Annals of Combinatorics 5 (3) p.347-362 June, 2001
AMS Subject Classification: 05A40, 05A30, 33D45
Abstract:
We introduce a translation operator which commutes with the Askey-Wilson operator and develop the corresponding theory of polynomials of binomial type and the Sheffer classification.
Keywords: continuous q -Hermite polynomials, q-translation, q-calculus, q-shift-invariant operators, generating functions, operator calculus, Sheffer sequences, polynomials of q-binomial type, q-A type zero

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