Liouville's Theorem and constant functions

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Skip over the 'branch cut' stuff. If you know f can be represented as a convergent power series, then just use it. Once you've actually figured out how the proof works then you can go back and try to write it without the series. I already said I can't tell you which part of your 'integral method' doesn't make sense. Because I can't find any parts that do make sense.
 
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