Laurent coefficient
= Laurent coefficient
{title2=$a_n=\frac{1}{2\pi i}\int_{|z-z_0|=r}\frac{f(z)}{(z-z_0)^{n+1}}\,dz$}
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>.