Let $\mathbb{C}$ be the
D1378: Standard complex metric space such that
| (i) |
$E \subseteq \mathbb{C}$ is a D78: Subset of $\mathbb{C}$
|
| (ii) |
\begin{equation}
E \neq \emptyset
\end{equation}
|
| (iii) |
$z_0 \in E$ is an D1387: Interior point of $E$ in $\mathbb{C}$
|
A
D4881: Complex function $f : E \to \mathbb{C}$ is
analytic at $z_0$ if and only if
\begin{equation}
\exists \, R > 0, a \in \mathbb{C}^{\mathbb{N}} : \forall \, z \in B(z_0, R) : f(z) = \lim_{N \to \infty} \sum_{n = 0}^N a_n (z - z_0)^n
\end{equation}
