Laurent theorem
= Laurent theorem
{c}
An analytic function on an annulus $r<|z-a|<R$ has a unique locally uniformly convergent expansion
$$
f(z)=\sum_{n=-\infty}^{\infty}c_n(z-a)^n,
\qquad
c_n=\frac1{2\pi i}\oint_C\frac{f(\zeta)}{(\zeta-a)^{n+1}}\,d\zeta,
$$
where $C$ is any positively oriented circle around $a$ in the annulus.