Series for q-sin sub q

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Theorem

The following formula holds for $|z|<1$: $$\sin_q(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k z^{2k+1}}{\langle 1;q \rangle_{2k+1}},$$ where $\sin_q$ denotes the $\sin_q$ function.

Proof

References