Existence of Laurent Series

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

$$\sum_{j=-\infty}^\infty a_j (z-z_0)^j \ $$

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