Relationship between csch and csc

Theorem

The following formula holds: $$\mathrm{csch}(z)=i \csc(iz),$$ where $\mathrm{csch}$ denotes the hyperbolic cosecant and $\csc$ denotes the cosecant.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.10$