\begin{definition}[Definition:Analytic Continuation]
Let $U \subset \C$ be an open set.
Let $f: U \to \C$ be an analytic function.
Let $V$ be an open subset of $\C$ such that $U \subset V$.
An '''analytic continuation of $f$ to $V$''' is an analytic function $F: V \to \C$ such that $\map F z = \map f z$ for $z \in U$.
\end{definition}