Hi, I was wondering about how to determine the residue of a pole that is written in the form:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f(z) = \frac{1}{(1 + t^r)^{\frac{m}{r}}}[/tex]

Here:

[tex]m \in \mathbb{N}\,\,\,\,\;\,\,\,\,r \in \mathbb{R}[/tex]

And if it's possible, r could be complex.

Would the order of the pole bem? Implying that the r's cancel each other out? Would this give the usual residue theorem:

[tex]res(f, e^{\frac{\pi}{r}i}) = \frac{1}{(m-1)!} \lim_{z \to e^{\frac{\pi}{r}i}} \frac{d^{m-1}}{dz^{m-1}} (z - e^{\frac{\pi}{r}i})^{m} f(z)[/tex]

Or does the residue theorem fail all together here? If so, then, is there any way other way of solving the integral:

[tex]\int_{C} f(z)dz[/tex]

WhenCis a simple closed contour with the pole inside of it. Any help would be greatly appreciated. I didn't post this in the homework section because it isn't a homework question, just a question of intrigue and research. Thanks.

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# A question regarding the order of a pole

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