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An expression in functional analysis

  1. May 23, 2010 #1
    Are there any theorems concerning this expression
    [tex]\frac{1}{z}f\left(\frac{1}{z}\right)[/tex]. I appreciate posts of any theorems you can think of.
  2. jcsd
  3. May 23, 2010 #2


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    Homework Helper

    The closest thing I can think of concerns [itex]f(1/z)/z^2[/itex]. If you have a complex function f(w) with a pole at infinity, then

    [tex]\mbox{Res}_{w = \infty} f(w) = -\mbox{Res}_{z = 0} \frac{f(\frac{1}{z})}{z^2}[/tex]
  4. May 24, 2010 #3
    Thanks, this was exactly what I was looking for!
  5. May 24, 2010 #4


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    Science Advisor

    Haha, sometimes a vague question can get the perfect answer immediately :)
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