Tanhc
From specialfunctionswiki
The $\mathrm{tanhc}$ function is defined by $$\mathrm{tanhc}(z) = \dfrac{\mathrm{tanh}(z)}{z}.$$
Domain coloring of analytic continuation of $\mathrm{tanhc}(z)$.
Properties
Theorem: The following formula holds: $$\dfrac{d}{dz} \mathrm{tanhc}(z) = \dfrac{\mathrm{sech}^2(z)}{z}-\dfrac{\mathrm{tanh(z)}}{z^2}.$$
Proof: █
