About multiplying two essential singularity containing functions

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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?

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For example, $e^{1/z}$ multiplied by $e^{-1/z}/z^7$ yields $1/z^7$.