For $n\ge1$, $f=z^ne^{n/z}$ is <holomorphic> at every finite nonzero point. At zero its <Laurent series> has infinitely many negative powers, so zero is an <essential singularity>. If the <Riemann sphere> is included, $f(1/w)=w^{-n}e^{nw}$ has a <pole> of order $n$ at $w=0$, so infinity is a <pole> of order $n$.

Solution

Past exam of the short options paper shared by Parts A and B of the physics course of the University of Oxford / 2019 / S1 / 2 / a / Solution

 Solution (source code)