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How do singularities of a function on a complex plane affect real line behavior?

  1. Oct 9, 2007 #1

    Simfish

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    Gold Member

    consider the function

    [tex]\frac{1}{\epsilon^2 + z^2}[/tex]

    So we know that there are two poles, one at [tex]z = i \epsilon[/tex], one at [tex]z = - i \epsilon[/tex]. So when this function never hits 0 on the real line, how do the singularities affect its behavior on the line?

    Okay, so poles are a subclass of singularities. I think that [tex]z = i \epsilon[/tex] and [tex]z = - i \epsilon[/tex] are poles - I may be wrong here. The question is - how do complex singularities (complex poles in this case) affect a function's behavior when the function is plotted on the real line?
     
    Last edited: Oct 9, 2007
  2. jcsd
  3. Oct 9, 2007 #2

    mathwonk

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    they determine the radius of convergence of the real taylor series for the function, in this case it is e, about x=0.
     
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