Relationship between coth and cot

Theorem

The following formula holds: $$\coth(z)=i\cot(iz),$$ where $\coth$ denotes the hyperbolic cotangent and $\cot$ denotes the cotangent.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.12$