I have been studying complex integration for a few months now, and it seems my textbook mostly considers integration on closed contours.
Is there no interest in integration on non-closed contours ?
2026-04-03 04:17:22.1775189842
Complex integration: normally on a closed contour?
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To use residue theory, you need a closed contour. If you just have a non-closed contour, it may as well just be a line integral in $\mathbb{R}^2$. The whole point of complex integration theory is to apply the powerful machinery of Cauchy's theorem, and so given a regular integral you look for ways to close it in the complex plane.