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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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 .
The problem is showing exactly . If I can prove that its bounded on a punctured neighborhood of zero then this would follow.
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?
You could also try to write down the Laurent series:
You can factor out the and then evaluate the limit.
Originally Posted by EinStone Does L'Hopital rule also apply for holomorphic quotients?
Yes, it does.
And if I use it, how do I get to the result?
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