Taylor series of the exponential function
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Revision as of 06:20, 25 March 2016 by Tom (talk | contribs) (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 $z \in \mathbb{C}$: $$e^...")
Theorem: Let $z_0 \in \mathbb{C}$. The following Taylor series holds for all $z \in \mathbb{C}$: $$e^z = \displaystyle\sum_{k=0}^{\infty} \dfrac{(z-z_0)^k}{k!},$$ where $e^z$ is the exponential function.
Proof: █
