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[[de:Exponentialfunktion]]
[[fr:Exponentielle]][[pl:Funkcja_wyk%C5%82adnicza]]
The '''exponential function''' is one of the most important [[function]]s in [[mathematics]]. It is written as exp(''x'') or <math>e^x</math> (where ''e'' 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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:exp(''x'') is invertible with inverse exp(-''x'')
:the derivative of exp at the point ''x'' is that linear map which sends ''u'' to exp(''x'')·''u''.
In the context of non-commutative Banach algebras, such as algebras of matrices or operators on [[Banach space|Banach]] or [[Hilbert space|Hilbert]] spaces, the exponential function is often considered as a function of a real argument:
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