Relationship between tanh and tan

Theorem

The following formula holds: $$\tanh(z)=-i \tan(iz),$$ where $\tanh$ is the hyperbolic tangent and $\tan$ is the tangent.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.9$