Period of tanh

Theorem

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

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.15$