Singularity and residue

  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. HallsofIvy

    HallsofIvy 41,061
    Staff Emeritus
    Science Advisor

    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.
Know someone interested in this topic? Share this thead via email, Google+, Twitter, or Facebook

Have something to add?