= Solution
The <Laurent theorem> states that a <holomorphic function> on the <annulus> $R<|z-a|<S$ has a unique <Laurent series>
$$
\boxed{f(z)=\sum_{n=-\infty}^{\infty}c_n(z-a)^n,\qquad c_n=\frac1{2\pi i}\int_{|\zeta-a|=\rho}\frac{f(\zeta)}{(\zeta-a)^{n+1}}\,d\zeta,\quad R<\rho<S.}
$$
The integration circle is counterclockwise. The series converges absolutely at every point of the annulus and uniformly on every compact subannulus. The <coefficient> <integrals> are independent of the choice of $\rho$ by the <Cauchy integral theorem> applied between two such circles. These statements include $R=0$ or $S=\infty$ when the indicated annulus has those endpoints.
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