Existence of Laurent Series

Theorem
Let $f: \C \to \C$ be a function and $z_0 \in U \subset \C$ such that $f$ is analytic in $U - \left\{{z_0}\right\}$.

Then there is a Laurent series


 * $\displaystyle \sum_{j=-\infty}^\infty a_j \left({z - z_0}\right)^j$

such that the sum converges to $f$ in $U - \left\{{z_0}\right\}$.