Difference between revisions of "Taylor series of the exponential function"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> Let $z_0 \in \mathbb{C}$. The following Taylor series holds for all $z \in \mathbb{C}$: $$e^...") |
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| − | + | ==Theorem== | |
| − | + | The following [[Taylor series]] holds for all $z \in \mathbb{C}$: | |
| − | $$e^z = \displaystyle\sum_{k=0}^{\infty} \dfrac{ | + | $$e^{z} = \displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{k!},$$ |
where $e^z$ is the [[exponential function]]. | where $e^z$ is the [[exponential function]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 04:03, 3 October 2016
Theorem
The following Taylor series holds for all $z \in \mathbb{C}$: $$e^{z} = \displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{k!},$$ where $e^z$ is the exponential function.
