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Integrals of the function f(z) = e^(1/z) (complex analysis)

  1. Apr 16, 2015 #1
    How do you integrate f(z) = e^(1/z) in the multiply connected domain {Rez>0}∖{2}

    It seems like integrals of this function are path independent in this domain since integrals of e^(1/z) exist everywhere in teh domain {Rez>0}∖{2}. Is that correct?
     
    Last edited: Apr 16, 2015
  2. jcsd
  3. Apr 16, 2015 #2

    mfb

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    I agree.
    Where is the point in excluding that point, by the way? It is not special.
     
  4. Apr 17, 2015 #3

    Svein

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    I seem to remember that the function given by f(z)=0 for Re(z)≤0 and [itex]f(z)=e^{-\frac{1}{z}} [/itex] for Re(z)>0 is ℂ in the whole complex plane, but not analytic...
     
  5. Apr 17, 2015 #4

    mfb

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    Why?
    The Laurent series is easy to construct here.
     
  6. Apr 18, 2015 #5

    Svein

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    Sorry, that should be C.
     
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