Residues are complex numbers that arise in the context of meromorphic functions, specifically relating to the behavior of these functions near their poles. The residue at a pole is the coefficient of the $(z - z_0)^{-1}$ term in the Laurent series expansion of the function around that pole. Understanding residues is crucial for evaluating contour integrals and applying the residue theorem, which connects residues with the evaluation of integrals over closed curves.
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