- #1

marcusl

Science Advisor

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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.

[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.