Taylor series of the exponential function

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Theorem

Let $z_0 \in \mathbb{C}$. The following Taylor series holds for all $z \in \mathbb{C}$: $$e^{z} = \displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{k!},$$ where $e^z$ is the exponential function.

Proof

References