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: 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

    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


    User Avatar
    Science Advisor
    Gold Member
    2017 Award

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted