Inverse Gudermannian
From specialfunctionswiki
The inverse Gudermannian $\mathrm{gd}^{-1}$ is the inverse function of the Gudermannian function. It may be defined by the following formula for $x \in \mathbb{R}$: $$\mathrm{gd}^{-1}(x)=\displaystyle\int_0^x \dfrac{1}{\cosh(t)} dt,$$ where $\cosh$ denotes the hyperbolic cosine.
Graph of $\mathrm{gd}^{-1}$.
Domain coloring of $\mathrm{gd}^{-1}$.
