Definition:Exponential Function

Definition
The exponential function is denoted $\exp$ and can be defined in several ways, as described below.

For all definitions of the real exponential function:


 * The domain of $\exp$ is $\R$


 * The codomain of $\exp$ is $\R_{>0}$

For $x \in \R$, the real number $\exp x$ is called the exponential of $x$.

Complex Numbers
The definition still holds when $x \in \C$ is a complex number.

Equivalence of Definitions
As shown in Equivalence of Definitions of Exponential the definitions above are equivalent.

Also see

 * Basic Properties of Exponential Function

Linguistic Note
The word exponential derives ultimately from the (now archaic) verb to expone, which means to set forth, in the sense of to expound, or explain.

This itself comes from the Latin expono, meaning I expose, or I exhibit.

The word exponent (from which exponential is formed) therefore means a person (or statement) that explains something.