0
$\begingroup$

How to classify the singularities of $\sin\left(\frac{1}{\sin\pi z}\right)$. I think it should be essential singularities but I do not know how to prove it. To prove that it is not a pole nor a removable singularity I need to look at its limit at n, but how to do that?

$\endgroup$

1 Answer 1

1
$\begingroup$

Given $n \in \mathbb{Z}$, the limit of your expression as $z \to n$ along the real line (this is a real variable limit) clearly doesn't exist (even in the extended sense) and so each $n \in \mathbb{Z}$ is an essential singularity.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .