Complex analysis: Singularities
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