Exponential function: Difference between revisions

Revision as of 06:03, 5 May 2003

Revision as of 21:52, 11 May 2003

Line 1:

[[de:Exponentialfunktion]]

[[fr:Exponentielle]]

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

Line 46:

: <math>\exp(z + w) = \exp(z) \exp(w)</math>

: <math>\exp(0) = 1</math>

: <math>\exp(''z'') &\ne 0</math>

: <math>\exp&prime'(''z'') = \exp(''z'')</math>

for all ''z'' and ''w''. The exponential function on the complex plane is a [[holomorphic function]] which is periodic with imaginary period <math>2 \pi i</math> which can be written as