Definition:Analytic Continuation

Definition
Let $f: \C \to \C$ be an analytic function defined on some open set $U \subset \C$.

Let $V$ be an open subset of $\C$ such that $U \subset V$ and $F: \C \to \C$ is defined on $V$ satisfying $F \left({z}\right) = f \left({z}\right)$ for $z \in U$.

Then $F$ is an analytic continuation of $f$ to $V$.