Mathematics-Online lexicon: Exponential Function

	[home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff]
	Mathematics-Online lexicon:
	Exponential Function

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The exponential function can be defined as the limit of a sequence or a series:

$\displaystyle e^x = \exp(x)$	$\displaystyle =$	$\displaystyle \lim_{n\to\infty} (1 + x/n)^{n}$
	$\displaystyle =$	$\displaystyle \sum_{n=0}^\infty \frac{1}{n!} x^n\, .$

The exponential function is positive for all $x\in\mathbb{R}$ and it satisfies the functional equality

$\displaystyle e^{x+y} = e^x e^y\, .$

In particular $e^{-x}=1/e^x$ .

Graph of the exponential function:

$\includegraphics{graph_exp}$

see also:

automatically generated 4/ 7/2008