Exponential function: Difference between revisions

Revision as of 04:05, 24 March 2004

Revision as of 18:37, 8 April 2004

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[[de:Exponentialfunktion]]

[[fr:Exponentielle]][[pl:Funkcja_wyk%C5%82adnicza]]

The '''exponential function''' is one of the most important [[function (mathematics)|function]]s in [[mathematics]]. It is written as exp(<i>''x</i>'') or <i>e^x</i> (where <i>e</i> is the [[e (mathematical constant)|base of the natural logarithm]]) and can be defined in two equivalent ways, the first an [[infinite series]], the second a [[limit]]:

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: <math>e^x = \sum_{n = 0}^{\infty} {x^n \over n!} = 1 + x + {x^2 \over 2!} + {x^3 \over 3!} + {x^4 \over 4!} + ...\cdots</math>

: <math>e^x = \lim_{n \to \infty} \left( 1 + {x \over n} \right)^n</math>