The *residue* of a meromorphic function $f$ at some point $\zeta \in \mathbb{Z}$ is the coefficient of $(z - \zeta)^{-1}$ (the first order pole) of its Laurent series expansion around $\zeta$. Up to a prefactor, this is what is picked up by the contour integral around that point, accrding to the Cauchy integral formula.

- Wikipedia,
*Residue (complex analysis)*

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