Difference between revisions of "Q-exponential E sub q"
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Revision as of 03:58, 17 June 2016
If $|q|>1$ or the pair $0 < |q| <1$ and $|z| < \dfrac{1}{|1-q|}$ hold, then the $q$-exponential $E_q$ is $$E_q(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{[k]_q!},$$ where $[k]_q!$ denotes the $q$-factorial.
Properties
Meromorphic continuation of q-exponential E sub q
Q-difference equation for q-exponential E sub q
References
- 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): (6.150)
