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Evaluating Integrals using the Residue THM

  1. Dec 13, 2009 #1
    1. The problem statement, all variables and given/known data

    integral |z|=1 of sinz/z2dz

    2. Relevant equations
    Rule #1 if f(z) has a simple pole at z0, then
    Res[f(z),z0] = lim(as z goes to z0) (z - z0)*f(z)

    Rule #2 if f(z) has a double pole at z0, then
    Res[f(z),z0] = lim(as z goes to z0)d/dz (z - z0)2*f(z)

    Rule #3 If f(z) and g(z) are analytic at z0, and if g(z) has a simple zero at z0 then,
    Res[f(z)/g(z), z0] = f(z0)/g'(z0)

    Rule #4 If g(z) is analytic and has a simple zero at z0 then,
    Res[1/g(z), z0] = 1/g'(z0)

    3. The attempt at a solution

    Just confused on which one to use? Would I integrate first? And if so what would my z0 be in Rest[..., z0]

  2. jcsd
  3. Dec 13, 2009 #2
    What kind of of pole does the function sinz/z2 have and where is it? Although I think 1 and 2 will give the same result.
  4. Dec 13, 2009 #3
    double pole at i/2 and -i/2?

    Edit: Actually simple pole at z = 0?
    Last edited: Dec 13, 2009
  5. Dec 13, 2009 #4
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