Hi everyone, once I again I turn to all of your expertise in complex analysis.
Homework Statement
Evaluate
\int\frac{(ln(x))^{2}}{1+x^{2}}dx
from 0 to +infinity by appropriate series expansion of the integrand to obtain
4\sum(-1)^{n}(2n+1)^{-3}
where the sum goes from n=0 to...
Homework Statement
Determine the nature of the singularities of the following function and evaluate the residues.
\frac{z^{-k}}{z+1}
for 0 < k < 1
Homework Equations
Residue theorem, Laurent expansions, etc.
The Attempt at a Solution
Ok this is a weird one since we've...
Ok I'll accept it ;)
That makes sense. Now I feel more confident with the result of zero.
Thanks again, both of you, I've gone crazy over this one problem!
Take care,
-Mike
Thanks for all the help guys,
I applied cauchy's integral formula on both integrals and I also got zero.
Using: \oint\frac{dz}{z-1}
I let f(z)=1, and f eval'd at the singularity is obviously f(1)=1, so I said
\oint\frac{dz}{z-1} = 2\pii(1) = 2\pii
Likewise, I got the same answer for the...
Well I don't understand how that works since the domain still has two singularities. Are you suggesting apply cauchy's integral formula one at a time. Is that valid? I'm new to the topic and trying to get my head around it. I'll try it out to see what I get.
Contour integral with multiple singularities inside domain without residue theorem??
Homework Statement
Evaluate
\oint\frac{dz}{z^{2}-1}
where C is the circle \left|z\right| = 2
Homework Equations
Just learned contour integrals, so not much.
Ok to use Cauchy's Integral formula (if...