# Sech

The hyperbolic secant function $\mathrm{sech} \colon \mathbb{R} \rightarrow (0,1]$ is defined by $$\mathrm{sech}(z)=\dfrac{1}{\cosh(z)},$$ where $\cosh(z)$ denotes the hyperbolic cosine. Since this function is not one-to-one, we define the inverse hyperbolic secant function as the inverse function of $\mathrm{sech}$ restricted to $[0,\infty)$.