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}