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Need help with finding residue of a simple function

  1. Oct 20, 2009 #1
    Need help with finding residue of a "simple" function

    Hello,
    I'm trying to find the residue z=0 of f(z) = (1 + z)e^(3/z)

    I understand this is a essential singularity. I know the answer is 15/2 but I can't seem to find the solution.

    I've tried this so far:

    f(z) = (1 + z) ( (3/z) + 9/2z² + ...)
    But now i'm stuck ! please help :)
     
  2. jcsd
  3. Oct 20, 2009 #2

    Mute

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    Re: Need help with finding residue of a "simple" function

    Do you know what the residue is? You've expanded the exponential in a series - why? It's the correct thing to do, but do you know why?

    It's because the residue of a function at [itex]z = 0[/itex] is given by the coefficient of [itex]1/z[/itex] in its Laurent series expansion. So, what's the coefficient of 1/z in your series expansion? (You have to multiply your two series together!)
     
  4. Oct 20, 2009 #3
    Re: Need help with finding residue of a "simple" function

    Aha !
    I'm going to study the Laurent series expansion part again... ;)

    Thank you ! :)
     
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