Difference between revisions of "Taylor series for sinh"
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| − | + | ==Theorem== | |
| − | + | The following [[Taylor series]] holds for all $z \in \mathbb{C}$: | |
$$\sinh(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{z^{2k+1}}{(2k+1)!},$$ | $$\sinh(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{z^{2k+1}}{(2k+1)!},$$ | ||
where $\sinh$ is the [[sinh|hyperbolic sine]]. | where $\sinh$ is the [[sinh|hyperbolic sine]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 07:53, 8 June 2016
Theorem
The following Taylor series holds for all $z \in \mathbb{C}$: $$\sinh(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{z^{2k+1}}{(2k+1)!},$$ where $\sinh$ is the hyperbolic sine.
