Need help with Caucy Integral

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  • #1
marcusl
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Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
mathwonk
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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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