Past exam of the algebra, analysis and differential equations II course of the University of Oxford / 2012 / 5 / b / i

An isolated singularity at $z_0$ means that some radius $r>0$ has $f$ holomorphic on the punctured disk $0<|z-z_0|<r$, while $f$ is not initially defined as a holomorphic function at $z_0$. The adjective isolated refers to the absence of other singularities in this punctured neighbourhood; it permits a removable singularity.