Laurent coefficient ($a_n=\frac{1}{2\pi i}{\int }_{|z-z_0|=r}\frac{f(z)}{(z-z_0{)}^{n+1}}dz$)

A Laurent coefficient is a coefficient $a_n$ in the Laurent series $f(z)={\sum }_{n\in \mathbb{Z}}{a}_n(z-z_0{)}^n$ of a holomorphic function on an annulus. Integration around a circle in the annulus gives the displayed formula, including negative indices. The coefficient $a_{-1}$ is the residue.