Recent content by newmike

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...

Ok, I used this and still got zero. I'm going to try use cauchy's integral formula on each one as you both are suggesting. Thanks again.

Ok, let me see if that changes things. Thanks.

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...