2. Definition-Proposition 2.11.1 - Meromorphic functions with finitely many poles

Let $f : G \to C$ be a meromorphic function with finitely many poles in $G$ , say $ℓ$ . Let $h_{i}$ , $1 \leq i \leq ℓ$ be the principal part of the Laurant series around the pole $z_{i} \in G$ . Then we can consider the function:

f (z) - \sum_{i = 1}^{ℓ} h_{i} (z)

is 1;;holomorphic on $G$ , if we fill in the removable singularities.