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

Can you offer guidance or do you also need help?
Draft saved Draft deleted