1. Not finding help here? Sign up for a free 30min 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!

Cauchy's Integral Formula problem

  1. Oct 2, 2008 #1
    How would you integrate sin(z)/(z-1)^2 using Cauchy's Integral Formula? 1 is in C.

  2. jcsd
  3. Oct 2, 2008 #2
    Integration domain would be relevant.
  4. Oct 2, 2008 #3
    All it says is that "C is any simple closed contour around both z = 1 and z = i"
  5. Oct 2, 2008 #4
    The knowledge that the contour goes once around z=1 should be enough. The comment on point z=i looks like misdirection.

    I believe that actually you already know what you want there, assuming that you know the Cauchy's integral formula. It's just that the 1/(z-1)^2 is confusing?
  6. Oct 2, 2008 #5
    Yeah. I know the formula.

    I did 1/(z-1)^2 but didn't come out as partial fractions.
  7. Oct 2, 2008 #6
    There exists coefficients [itex]a_{-2}, a_{-1}, a_0, a_1, \ldots[/itex] so that

    \frac{\sin z}{(z-1)^2} = \frac{a_{-2}}{(z-1)^2} \;+\; \frac{a_{-1}}{z-1} \;+\; a_0 \;+\; a_1(z-1) \;+\; \cdots

    For integration, you need to know the [itex]a_{-1}[/itex].
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Cauchy's Integral Formula problem