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I'm trying to classify the type of singularity at z = ∞ (the point at infinity) of the complex function:

click to see the equation

Up to now, I've just been able to prove that ∞ is not a pole. So I would like to prove that it is either an essential singularity or a removable singularity. Thank you for your suggestions!

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  • $\begingroup$ See what happens when you put $z=n \ge 2$ and then $z=in$ $\endgroup$ – Conrad Oct 23 '20 at 13:54
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At , $z=n$ for each $1\neq n\in\mathbb{N}$ , $f(z)$ have zeros.

As, limit point of zeros is a isolated essential singularity.

So, $z=\infty$ is a isolated essential singularity of $f(z)$.

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  • $\begingroup$ I don't understand what are you saying? And by the way, the given function is undefined at $z=\infty$. Also, one thing , a complex function is well defined at $\infty$ only if function is constant. $\endgroup$ – A learner Oct 23 '20 at 16:48

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