Difference between revisions of "Exponential"
From specialfunctionswiki
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| − | File:Exponentialplot.png|Graph of $\exp | + | File:Exponentialplot.png|Graph of $\exp$. |
File:Complexexponentialplot.png|[[Domain coloring]] of $\exp$. | File:Complexexponentialplot.png|[[Domain coloring]] of $\exp$. | ||
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Revision as of 03:52, 6 June 2016
The exponential function $\exp \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by the formula $$\exp(z) = e^z = \sum_{k=0}^{\infty} \dfrac{z^k}{k!},$$ where $e$ is the base of the natural logarithm.
Graph of $\exp$.
Domain coloring of $\exp$.
Properties
Derivative of the exponential function
Taylor series of the exponential function
Exponential in terms of hypergeometric 0F0
Euler E generating function
Continued fraction for 1/sqrt(pi) integral from -infinity to infinity of e^(-t^2)/(z-t) dt
