Relationship between sech and sec

Theorem

The following formula holds: $$\mathrm{sech}(z)=\sec(iz),$$ where $\mathrm{sech}$ denotes the hyperbolic secant and $\sec$ denotes the secant.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.11$