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Complex Analysis - Rational Functions

  1. May 8, 2013 #1
    1. The problem statement, all variables and given/known data
    I'm studying for my final exam and came across this problem:
    Let f and g be entire analytic functions and |f(z)|<|g(z)| when |z|>1. Show that f/g is a rational function.

    3. The attempt at a solution
    I really have no clue where to go :(
  2. jcsd
  3. May 10, 2013 #2
    Well, you know that since |f(z)|<|g(z)| on |z|>1, f(z)/g(z) is bounded on |z|>1. Does this tell you anything?
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