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Homework Help: 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].
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