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Laurent series

{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.

Laurent theorem

Past exam of the mathematics course of the University of Cambridge / 2018 / ib / Paper 2 / 13A / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 1 / 12G / a / Solution

Laurent theorem

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Laurent theorem

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