Definition:Inverse Hyperbolic Sine/Real/Definition 2

Definition
The inverse hyperbolic sine $\sinh^{-1}: \R \to \R$ is a real function defined on $\R$ as:


 * $\forall x \in \R: \map {\sinh^{-1} } x := \map \ln {x + \sqrt {x^2 + 1} }$

where:
 * $\ln$ denotes the natural logarithm of a (strictly positive) real number
 * $\sqrt {x^2 + 1}$ denotes the positive square root of $x^2 + 1$.

Also known as
The inverse hyperbolic sine function is also known as the hyperbolic arcsine function.

Also see

 * Equivalence of Definitions of Real Inverse Hyperbolic Sine