Let $U \subseteq \mathbb{C}$ be an D5008: Standard open complex set such that

(i)	\begin{equation} U \neq \emptyset \end{equation}

A D4881: Complex function $f : U \to \mathbb{C}$ is analytic at $z_0 \in U$ if and only if \begin{equation} \exists \, R > 0 \text{ and } a \in \mathbb{C}^{\mathbb{N}} : \forall \, z \in \mathbb{C} \left( |z - z_0| < R \quad \implies \quad f(z) = \sum_{n = 0}^{\infty} a_n (z - z_0)^n \right) \end{equation}