Singularity and residue

  1. Nov 1, 2007 #1
    1. The problem statement, all variables and given/known data
    Do residues exist only for holomorphic function?

    Classify the singularity and calculate the residue of tanh(z) and tan(z)

    3. The attempt at a solution
    For both
    Essential isolated singularity because the numerator has an infinite number of terms.

    Residue = 0.
    Last edited: Nov 1, 2007
  2. jcsd
  3. Nov 1, 2007 #2


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    What are the definitions of "residue" and "holomorphic function"?

    At what point do tanh(z) and tan(z) have an isolated singularity? It doesn't make sense to talk about the "residue" of a function. A function may have a "residue" at a specific point.
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