Hello. I am looking at the following problem:

Let be holomorphic in so that

Prove that is a removable singularity.

I'd like to use the Gauss Mean Value Property, where

Then I could try to put a bound on and conclude that the singularity is removable. However, the Gauss Mean Value property only works if the function is holomorphic on a simply connected domain.

I was wondering if there are any suggestions on how to approach this problem. Any ideas would be much appreciated.