19.5 Residue Theorem


We saw in the last section that if the complex function f has an isolated singularity at the point z0, then f has a Laurent series representation

which converges for all z near z0. More precisely, the representation is valid in some deleted neighborhood of z0, or punctured open disk, 0 < |zz0| < R. In this section our entire focus will be on the coefficient a−1 and its importance in the evaluation of contour integrals.


The coefficient a−1 of 1/(zz0) in the Laurent series given above is called ...

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