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

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

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

Notation
The exponential of $x$, $\exp x$, is frequently written as $e^x$. The consistency of this power notation is demonstrated in Exp x equals e^x for Rational Numbers.

Also see

 * Properties of Exponential Function
 * Properties of Complex Exponential Function