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Math Help - complex analysis

  1. #1
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    complex analysis

    Hey guys.
    Look at this question please.
    I have two paths, and I need to proof the thing in red.
    They give a tip due, they say to show first that the equation in green is correct and then using Taylor development, to proof the red equation.
    I'm still in the first phase, in the green equation. I know it got something to do with Cauchy's integral formula but I cant see how...
    Any idea guys?

    Thanks a lot.
    Attached Thumbnails Attached Thumbnails complex analysis-1.jpg  
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  2. #2
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    Anchorage, AK
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    Consider the poles of \frac{e^iz}{z^2+a^2} in the complex plane. What are the residues, and which ones are enclosed in your contour (a semi-circle of radius R in the upper half plane)?

    --Kevin C.
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  3. #3
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    Quote Originally Posted by TwistedOne151 View Post
    Consider the poles of \frac{e^iz}{z^2+a^2} in the complex plane. What are the residues, and which ones are enclosed in your contour (a semi-circle of radius R in the upper half plane)?

    --Kevin C.
    I'm sorry but I'm not familiar with this terms (residues and such) because of my English.
    Anyway, this is what I did (in the pic) and I used Cauchy's integral formula to calculate the integral but I'm not sure what it gave me.
    I can't see how I can prove the equation in green using these.
    Can I get some more tips?

    Thanks a lot.
    Attached Thumbnails Attached Thumbnails complex analysis-1.jpg  
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