1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Very easy and quick residue calculus question.

  1. Apr 27, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]\oint_{\left|z\right|=3/2} \frac{e^{\frac{1}{z-1}}}{z} dz
    [/tex]

    2. Relevant equations

    Using residue theorem, since there are two singularities withing the domain, evaluate residues at each singularity, and multiply by [tex]2\pi i[/tex]

    3. The attempt at a solution

    Here is the problem. The answer is [tex]2 \pi i[/tex] instead of [tex]2 \pi i + \frac{2\pi i}{e}[/tex]
    I don't understand why singularity at zero is ignored.
    FYI, if the domain it |z| = 1/2, the answer is 2pi*i/e.
     
  2. jcsd
  3. Apr 28, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    They didn't ignore the singularity at 0. The singularity at z=1 is not what you think it is. Try putting w=z-1 and expanding the power series around w=0. You'll find an infinite number of 1/w terms. Sum them.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Very easy and quick residue calculus question.
  1. Very easy question (Replies: 3)

Loading...