Definition:Analytic Continuation

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

If $$V \ $$ is also an open subset of $$\C \ $$ such that $$U \subset V \ $$ and $$F:\C \to \C \ $$ is defined on $$V \ $$ satisfying $$F(z)=f(z) \ $$ for $$z \in U \ $$, then $$F \ $$ is an analytic continuation of $$f \ $$ to $$V \ $$.