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Need help with Caucy Integral

  1. Mar 18, 2007 #1


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    I have a function
    [tex]G_0=\frac{1-\alpha/u^2}{1-\alpha u^2} .[/tex]

    Since [tex]0<\alpha<1[/tex], [tex]G_0[/tex] has zeroes but no poles inside the unit circle.

    I need to evaluate
    [tex]\Gamma(\tau)=\frac{1}{2\pi i}\oint{\frac{\ln{G_0 (u)}}{u-\tau}du}[/tex]
    where the integral is around the unit circle. How do I evaluate the poles of the integrand so I can evaluate this using residues?

    EDIT: Oops, G0 has a second order singularity at u=0, too.
  2. jcsd
  3. Mar 20, 2007 #2


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    maybe power series wouldwork, first the geometric series for G0 then the series for log(1+w)?
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