An <essential singularity> is an <isolated singularity> that is neither removable nor a <pole>. In terms of the <Laurent series> this means $\boxed{\text{infinitely many negative-power coefficients are nonzero}}$: no finite multiplication by a power of $z$ removes the singularity.

Solution

Past exam of the algebra, analysis and differential equations II course of the University of Oxford / 2010 / Analysis / 5 / b / iii / Solution

 Solution (source code)