https://tube.cosmicflow.space/videos/watch/00d41844-3a87-4fa2-accb-ca3e0bc815ad 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 https://www.youtube.com/playlist?list=PL8yHsr3EFj537_iYA5QrvwhvMlpkJ1yGN Mon, 19 Oct 2026 20:06:58 GMT https://validator.w3.org/feed/docs/rss2.html PeerTube - https://tube.cosmicflow.space https://tube.cosmicflow.space/lazy-static/avatars/8891227d-e60f-40aa-88be-4c856c6a73dc.png https://tube.cosmicflow.space/videos/watch/00d41844-3a87-4fa2-accb-ca3e0bc815ad All rights reserved, unless otherwise specified in the terms specified at https://tube.cosmicflow.space/about and potential licenses granted by each content's rightholder.