-5
votes
1answer
75 views

computing integral of dz/(z+1) on unit circle [on hold]

I guess it must be a simple matter in complex analysis, but I would like to compute the the following integral: $$ \oint_C\frac{dz}{z+1} $$ and $$ \int_C\frac{dz}{z+1} $$ where $C=\{z\in \mathbb{C}: ...
1
vote
0answers
150 views

complex contour integral calculation after Möbius transformation

Good day to everyone. In my scientific research I've got stuck with a contour integration problem. I would like to evaluate the following integral: $$I=\int_0^{\infty } \frac{e^{\frac{\alpha -\mathrm ...
0
votes
0answers
272 views

Help with an irregular integral

I am looking for help with doing the following integral : $$\frac{1}{2\pi i}\int_{1}^{\infty}\ln\left(\frac{1-e^{-2\pi i x}}{1-e^{2\pi i x}} \right )\frac{dx}{x\left(\ln x+z\right)}\;\;\;\;z\in ...
1
vote
0answers
273 views

Residue Cancellation

I am trying to understand how to apply the residue theorem to solve $\frac{1}{2\pi j}\int^{\gamma+j\infty}_{\gamma-j\infty}\Gamma(n-s)\Gamma(s)\Gamma(1-s) {}_1F_1(s;b;c) ...