1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted