# Definition:Exponential Function/Real/Power Series Expansion

## Definition

Let $\exp: \R \to \R_{>0}$ denote the (real) exponential function.

The exponential function can be defined as a power series:

$\exp x := \ds \sum_{n \mathop = 0}^\infty \frac {x^n} {n!}$

The number $\exp x$ is called the exponential of $x$.