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Complex Analysis/Radius of Convergence question.

  1. Apr 3, 2017 #1
    1. The problem statement, all variables and given/known data
    Question asks to show that if f is an entire function and bounded then it is polynomial of degree m or less.

    2. Relevant equations
    media%2Fa8d%2Fa8dc1d29-deb9-41c2-8537-b890cd541afc%2FphpscTgqj.png

    3. The attempt at a solution
    I tried plugging in the power series for f(z) and tried/know it is related to Liouville's Theorem somehow but I am just not gaining any traction. A picture of the question is attached below: media%2Ff03%2Ff03104be-cddf-4510-8fee-46acd2526ce3%2Fphpx1dieD.png
     
  2. jcsd
  3. Apr 3, 2017 #2

    FactChecker

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    Science Advisor
    Gold Member

    Make r big.
    Your statement of the problem is wrong if you really mean the inequality of question 21 (in your attempt at a solution). A bounded entire function is a constant.
     
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