# Q-exponential e sub q

The $q$-exponential $e_q$ is defined for $|z|<1$ by the formula $$e_q(z) =\displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{(q;q)_k},$$ where $(q;q)_k$ denotes the q-shifted factorial. Note that this function is different than the $q$-exponential $e_{\frac{1}{q}}$.