ThmDex – An index of mathematical definitions, results, and conjectures.
F12371
Formulation 0
Let $\sinh$ be the D1934: Standard natural hyperbolic sine function.
Let $\cosh$ be the D1933: Standard natural hyperbolic cosine function.
The standard natural hyperbolic tangent function is the D4364: Real function \begin{equation} \tanh : \mathbb{R} \to (-1, 1), \quad \tanh(x) = \frac{\sinh(x)}{\cosh(x)} \end{equation}