Let $G\subseteq \mathbb{C}$ be a domain. A partial function $f:G\to \mathbb{C}$ is called meromorphic if it is holomorphic in $G$ up to 1;;possible poles. Equivalently, if $f:G\to \hat{\mathbb{C}}$ is holomorphic, with our definition of differentiation at infinity, then we say $f:G\to \mathbb{C}$ is meromorphic.