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Math Help - Cauchys Derivative Formula

  1. #1
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    Cauchys Derivative Formula

    Hi.

    Evaluate the integral with respect to C, C={ z: lz+2l = 3}, Integrate cos(pi*z)/( ((z+4)^2)*(z-2).dz

    I understand that from the denominator the value -4 lies inside C but the point 2 does not.

    Am i right in thinking then f(z)=(cos(pi*z)) / ((z-2)^2) is analytic on R and C is a simple closed contour in R. Hence by Cauchy's First Derivative Formula......

    ....and this is where I'm unsure.

    Any suggestions?

    Shoni
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  2. #2
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    Re: Cauchys Derivative Formula

    If there is a singularity in your region, then no, it is not a simple closed contour. You will need to evaluate residues.
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  3. #3
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    Re: Cauchys Derivative Formula

    What does that mean exactly to "evaluate the residues?" Please could you show me using the example?

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