Difference between revisions of "Q-sin sub q"
From specialfunctionswiki
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Revision as of 21:20, 4 July 2016
The function $\sin_q$ is defined by $$\sin_q(z)=\dfrac{e_q(iz)-e_q(-iz)}{2i} = \displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^kz^{2k+1}}{(q;q)_{2k+1}},$$ where $e_q$ denotes the $q$-exponential $e$ and $(q;q)_{2k+1}$ denotes the $q$-Pochhammer symbol.
