Difference between revisions of "Taylor series of the exponential function"
From specialfunctionswiki
| Line 1: | Line 1: | ||
| − | + | ==Theorem== | |
| − | + | Let $z_0 \in \mathbb{C}$. The following [[Taylor series]] holds for all $z \in \mathbb{C}$: | |
$$e^z = \displaystyle\sum_{k=0}^{\infty} \dfrac{(z-z_0)^k}{k!},$$ | $$e^z = \displaystyle\sum_{k=0}^{\infty} \dfrac{(z-z_0)^k}{k!},$$ | ||
where $e^z$ is the [[exponential function]]. | where $e^z$ is the [[exponential function]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
Revision as of 03:46, 6 June 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.
