We examine the properties of a family of q-exponential functions, which depend on an extra parameter . These functions have a well defined meaning for both the 0 < |q| < 1 and |q| > 1 cases if only . It is shown that any two members of this family with different values of the parameter are related to each other by a Fourier - Gauss transformation.
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Natig M. Atakishiyev (1996) studied this question.
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