# Period of sinh

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## Theorem

The following formula holds for all $k \in \mathbb{Z}$: $$\sinh(z+2k\pi i)=\sinh(z),$$ where $\sinh$ denotes the hyperbolic sine, $\pi$ denotes pi, and $i$ denotes the imaginary number.

## Proof

## References

- 1964: Milton Abramowitz and Irene A. Stegun:
*Handbook of mathematical functions*... (previous) ... (next): $4.5.13$