1
$\begingroup$

Let $a$ be a point on the complex plane such that the function $f$ has an essential singularity. I am trying to prove that the square of that function also has an essential singularity.

I suppose that it does not have an essential singularity. Then $\exists ;k$ such that $(z-z_0)^{2k}f^2(z)$ differentiable. Then if I could take the square root and preserve the differentiability I would have finised. Can I do that?

$\endgroup$
  • $\begingroup$ can you apply the Weirstrass theorem? $\endgroup$ – vnd Jan 11 '16 at 2:30
3
$\begingroup$

Suggestion. Another, more convenient way to test if an isolated singularity of $f(z)$ at $z_0$ is not essential: $ (z- z_0)^k f(z) \to L$ for some $L$ in the extended complex plane.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.