ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
▼ Map
▼ Operation
▼ N-operation
▼ Binary operation
▼ Enclosed binary operation
▼ Groupoid
▼ Semigroup
▼ Standard N-operation
▼ Indexed sum
▼ Series
▼ Power series
▼ Convergent power series
▼ Natural complex exponential function
▼ Standard natural complex exponential function
▼ Standard natural complex hyperbolic sine function
▼ Standard natural hyperbolic sine function
Definition D6033
Standard natural hyperbolic tangent function
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}