Abstract
We give an overview of the remarkably simple transformation properties of the continuous q-Hermite polynomials Hn(x|q) of Rogers with respect to the classical Fourier integral transform. The behavior of the q-Hermite polynomials under the finite Fourier transform and an explicit form of the q-extended eigenfunctions of the finite Fourier transform, defined in terms of these polynomials, are also discussed.
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