Meaning of the complex residue

  1. Just spent the last few months working on an undergrad course in complex analysis and have a couple of things that aren't clear to me yet. One of them is the meanings of the residue of a complex function. I understand how to find it from the Laurent series and using a couple of other rules and I understand how it works with the residue theorem. But I still feel like there is a deeper interpretation out there waiting for me.......perhaps it's something geometrical?

    Grateful for any enlightened comment.
    :-)
     
  2. jcsd
  3. lurflurf

    lurflurf 2,325
    Homework Helper

    There are several equivalent ways to think about it. One is as the 1/(z-a) term of the laurent expansion. Another is the inner product of f with 1/(z-a). One could also think of it as the amount of (order 1) infinity at the point a.
     
  4. Thanks for that........the nearest I can get is that it could be 1/(2*pi) of a Dirac delta function with a pi/2 twist.
    :-)
     
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