Difference between revisions of "Series for q-sin sub q"
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Latest revision as of 15:39, 11 July 2016
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
- 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): $(6.201)$
