I recently did a problem in which the integral around a contour contained two residues, the sum of which was zero, so the total integral around the entire path was zero?(adsbygoogle = window.adsbygoogle || []).push({});

By the CIT, the function should then be analytic (holomorphic, if you like) inside that contour, but it isn't obviously since there are poles.

Why doesen't the CIT apply? Is the region no longer simply connected or something?

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# Cauchy integral theorem question

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