Difference between revisions of "Taylor series of the exponential function"
From specialfunctionswiki
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==Theorem== | ==Theorem== | ||
Let $z_0 \in \mathbb{C}$. The following [[Taylor series]] holds for all $z \in \mathbb{C}$: | Let $z_0 \in \mathbb{C}$. The following [[Taylor series]] holds for all $z \in \mathbb{C}$: | ||
| − | $$e^{z} = \displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{k!},$$ | + | $$e^{z} = \displaystyle\sum_{k=0}^{\infty} \dfrac{(z-z_0)^k}{k!},$$ |
where $e^z$ is the [[exponential function]]. | where $e^z$ is the [[exponential function]]. | ||
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[[Category:Theorem]] | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Revision as of 04:00, 3 October 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.
