I was wondering if there is a fast and easy way to classify isolated singularities rather than investigating the behaviour of the limit or the Laurent series. I understand that such shortcuts might not always work but they can be very handy.
I found that if we can write our function $f(z)$ as $f(z)=g(z)/(z-z_o)^m$ such that $g(z)$ is analytic and $g(z_0)$ is non-zero then $z_0$ is a simple pole of order m.
Are there any properties/shortcuts to determine whether the singularity is a removable singularity or an essential singularity.
Thank you.