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## Homework Statement

Show that if z

_{0}is an isolated singularity of f(z) that is not removable, then z

_{0}is an essential singularity for e

^{f(z)}.

## Homework Equations

z

_{0}is a pole of f(z) of order N iff f(z) = g(z)/(z-z

_{0})^N, where g is analytic at z

_{0}and g(z

_{0}) is not 0, iff 1/f(z) is analytic at z

_{0}and has a zero of order N, iff |f(z)| → ∞ as z → z

_{0}.

Casorati-Weierstrass theorem

## The Attempt at a Solution

## Homework Statement

I know what to do if z is an essential singularity. But I'm having trouble if z is a pole. It seems that what I must do is find a sequence of points going to z

_{0}such that f(z) goes to infinity, and also a sequence of points going to z

_{0}such that f(z) approaches some complex number. I don't know how to do that.

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