Coth of a sum

Theorem

The following formula holds: $$\coth(z_1+z_2)=\dfrac{\coth(z_1)\coth(z_2)+1}{\cosh(z_1)+\coth(z_2)},$$ where $\coth$ denotes hyperbolic cotangent.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.27$