Quadratic 𝑞-exponentials and connection coefficient problems

Ismail, Mourad; Rahman, Mizan; Stanton, Dennis

doi:10.1090/S0002-9939-99-05017-0

Quadratic $q$-exponentials and connection coefficient problems
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by Mourad E. H. Ismail, Mizan Rahman and Dennis Stanton PDF

Proc. Amer. Math. Soc. 127 (1999), 2931-2941 Request permission

Abstract:

We establish expansion formulas of $q$-exponential functions in terms of continuous $q$-ultraspherical polynomials, continuous $q$-Hermite polynomials and Askey-Wilson polynomials. The proofs are based on solving connection coefficient problems.

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