1. Definition 2.4.1

Let $U \subseteq C$ be an open set, $f : U \to C$ holomorphic, and $z_{0}$ an isolated singularity of $f$ . Then the residue of $f$ at $z_{0}$ is defined as:
:?:

\underset{z = z_{0}}{R e s} f (z) := \frac{1}{2 π i} \oint_{| z - z_{0} | = ϵ} f (z) d z

Notice that this is also the coefficient of the $\frac{1}{x}$ term in the Laurant Series.