# Cauchy residue theorem

## Cauchy residue theorem

[kō·shē ′rez·ə‚dü ‚thir·əm] (mathematics)

The theorem expressing a line integral around a closed curve of a function which is analytic in a simply connected domain containing the curve, except at a finite number of poles interior to the curve, as a sum of residues of the function at these poles.

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