Holomorphic extension
= Holomorphic extension
{title2=$F|_U=f,\quad F\in\mathcal O(V),\quad U\subseteq V$}
A <holomorphic function> $F$ on a larger <open set> $V$ whose restriction to $U$ is the original <holomorphic function> $f$. A <removable singularity> is a point across which such an extension exists. On a <connected> larger <domain>, a <holomorphic extension> is unique by the <identity theorem>, provided $U$ is nonempty.