View source for Q-exponential e sub q

The $q$-exponential $e_q$ is defined for $0 < |q| <1$ and $|z|<1$ by the formula
$$e_q(z) =\displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{(q;q)_k}.$$
Note that this function is different than the [[q-exponential e sub 1/q |$q$-exponential $e_{\frac{1}{q}}$]].

=Properties=
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<strong>Theorem:</strong> The following formula holds:
$$e_q(z)=\dfrac{1}{(z;q)_{\infty}},$$
where $e_q$ is the [[Q-exponential e|$q$-exponential $e$]] and $(z;q)_{\infty}$ denotes the [[q-Pochhammer symbol]].
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<strong>Proof:</strong> █ 
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{{:Exponential e in terms of basic hypergeometric phi}}

{{:Q-Euler formula for e sub q}}

=References=
[http://www2.math.uu.se/research/pub/Ernst4.pdf The History of q-Calculus and a New Method]<br />