Hi,

I want to show that is bounded on some neighborhood of zero in the complex plane, for example on the unit circle. Any bound suffices, I have

but I don't know what to do now.

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- Apr 9th 2011, 04:39 PMEinStoneShow that function is bounded
Hi,

I want to show that is bounded on some neighborhood of zero in the complex plane, for example on the unit circle. Any bound suffices, I have

but I don't know what to do now. - Apr 9th 2011, 10:36 PMFernandoRevilla
We have so, defining the function is continuous on a closed unit disk centered at . As is a compact set, as an absolute maximum on .

- Apr 10th 2011, 02:53 AMEinStone
The problem is showing exactly . If I can prove that its bounded on a punctured neighborhood of zero then this would follow.

- Apr 10th 2011, 04:07 AMFernandoRevilla
L'Hopital rule.

- Apr 10th 2011, 09:00 AMEinStone
Does L'Hopital rule also apply for holomorphic quotients? I always thought its a real method. And if I use it, how do I get to the result?

- Apr 10th 2011, 11:53 AMroninpro
You could also try to write down the Laurent series:

You can factor out the and then evaluate the limit. - Apr 10th 2011, 12:13 PMFernandoRevilla