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Thread: Residue Theory

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    Residue Theory

    I am having trouble understanding how to calculate residues.

    I have the function

    [TEX]f(z)=\frac {z^a}{1+z^2}[/TEX] and am supposed to find

    [TEX]\int^\infty_0 f(z)\,dz[/TEX] using the keyhole contour. So I found singularities at +i and - i and am trying to find the residues there using

    [TEX]\lim_{z\to+i}\frac{{z^a}{(z-i)}}{1+z^2}[/TEX] and [TEX]\lim_{z\to-i}\frac{{z^a}{(z+i)}}{1+z^2} [/TEX]

    Is ths the right way to find residues? What are these limits?
    Last edited by monomocoso; 02-25-2012 at 04:28 PM.

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