Difference between revisions of "Taylor series of the exponential function"
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| − | <strong>Theorem:</strong> Let $z_0 \in \mathbb{C}$. The following [[Taylor series]] holds for all $z \in \mathbb{C}$: | + | <strong>[[Taylor series of the exponential function|Theorem]]:</strong> Let $z_0 \in \mathbb{C}$. The following [[Taylor series]] holds for all $z \in \mathbb{C}$: |
$$e^z = \displaystyle\sum_{k=0}^{\infty} \dfrac{(z-z_0)^k}{k!},$$ | $$e^z = \displaystyle\sum_{k=0}^{\infty} \dfrac{(z-z_0)^k}{k!},$$ | ||
where $e^z$ is the [[exponential function]]. | where $e^z$ is the [[exponential function]]. | ||
Revision as of 06:20, 25 March 2016
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: █
