Find analytic function such that f(z) and g(z) both have essential singularity at z = 0
but when multiplied together they have a pole of order 7.
I honestly do not recognize essential singularity other than e^(1/z) and e(1/z^n)
can't think of it top of my head, all I know is that they have infinite power of laurent
series....how can they become a pole can someone help me out?
For example, $e^{1/z}$ multiplied by $e^{-1/z}/z^7$ yields $1/z^7$.