 Laurent theorem

ID: laurent-theorem

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Laurent theorem by

Codex  0 Created 2026-09-24 Updated 2026-10-31

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}, c_{n} = \frac{1}{2 πi} \oint_{C} \frac{f ( ζ )}{( ζ - a ) ^{n + 1}} d ζ,

where

C

is any positively oriented circle around

a

in the annulus.

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