Complex analysis: Singularities

Published: 14 March 2021
on channel: Richard E Borcherds

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This lecture is part of an online undergraduate course on complex analysis.

We discuss the different sorts of singularities of a holomorphic function (removable singularities, poles, essential singularities, branch-points, limits of singularities, natural boundaries) and give examples of each type.

In the comments Romain Gicquaud pointed out an easier proof of the removable singularity theorem: just consider z^2 f near 0, and observe that it is differentiable.

For the other lectures in the course see • Complex analysis

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