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Proof of Liouville's theorem - simple question

  1. Jul 29, 2013 #1
    1. The problem statement, all variables and given/known data
    i'm using Fisher's Complex Variables for my complex analysis class and there is a proof for Liouville's theorem. It says "Set g(z)=(F(z) - F(0)) / z; Then g is an entire function"

    2. Relevant equations

    3. The attempt at a solution
    I am confused by that statement. Doesn't g have a singularity at z=0? How can it be analytic over the entire complex plane?

    Thank you and sorry if it seems like a very stupid question.
  2. jcsd
  3. Jul 29, 2013 #2
    I don't have that particular complex book. So, I am not sure about that particular proof. But do you think that for the simple reason that as z tends to 0 you will end up with the indiscriminate form 0/0 has something to do with it?
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