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Taylor Series

  1. Aug 1, 2010 #1
    1. The problem statement, all variables and given/known data
    Let [tex]f(z)=\sum_{n=0}^{\infty} a_n z^n [/tex] be analytic at {z: |z|<R} and satisfies:
    [tex] |f(z)| \leq M [/tex] for every |z|<R.
    Let's define: d=the distance between the origin and the closest zero of f(z).

    Prove: [tex] d \geq \frac{R|a_0|}{M+|a_0|} [/tex].

    Hope you'll be able to help me

    Thanks !

    2. Relevant equations
    3. The attempt at a solution
    I've tried using Cauchy's Inequality... But it doesn't give anything new for [tex] a_0 [/tex].
    I've also tried isolating [tex] a_0 [/tex] from this inequality, but it gives me nothing...

    Hope someone will be able to help me

    Thanks in advance
  2. jcsd
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