Difference between revisions of "Exponential"
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File:Complex exp.jpg|[[Domain coloring]] of [[analytic continuation]] of $\exp$. | File:Complex exp.jpg|[[Domain coloring]] of [[analytic continuation]] of $\exp$. | ||
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Revision as of 04:16, 15 February 2015
The exponential function $\exp \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by the formula $$\exp(z) = e^z = \sum_{k=0}^{\infty} \dfrac{x^k}{k!},$$ where $e$ is the base of the natural logarithm. It can be characterized as the unique solution to the initial value problem $$\left\{ \begin{array}{ll} y'=y \\ y(0)=1. \end{array} \right.$$
- Exp.png
Graph of $\exp$ on $\mathbb{R}$.
- Complex exp.jpg
Domain coloring of analytic continuation of $\exp$.
