[[Complex analysis MOC]]
# Laurent series
The **Laurent series** of a complex function generalises the [[Taylor series]] to cover a many non-analytic functions
by taking including negative powers. #m/def/anal/comp
$$
\begin{align*}
f(z) = \sum_{n \in \mathbb{Z}} A_{n}(z-z_{0})^n
\end{align*}
$$
In the cases where $f(z)$ is [[Holomorphic function|holomorphic]],
this is identical to the [[Taylor series#Complex functions|Taylor series]] since $A_n = 0$ for all negative $n$.



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