1
vote
0answers
51 views

Integrating $\int_0^1 dx\,\ln(x-a)/(x-b)$ paying attention to cuts.

I am trying to compute the following integral, for complex $a$ and $b$ $$\int ^1 _0 dx \frac{\ln(x-a)}{x-b}$$ by turning it into something in terms of dilogarithms. But for certain values of $a$ ...
2
votes
0answers
211 views

Contour integral with branch point

As preparation for my exam I "invented" the following problem as an exercise to see whether I understand how to work with branch points. $f(z) = \frac{z}{\sqrt{z^2+1} (z^2 +a^2)}$ The goal is to ...
5
votes
2answers
481 views

Calculating integral with branch cut.

I'm learning how to calculate integrals with branch points using branch cut. For example: $$I=a\int_{\xi_{1}}^{\xi_{2}}\frac{d\xi}{(1+\xi^{2})\sqrt{\frac{2}{m}\left(E-U_{0}\xi^{2}\right)}}$$ where ...
1
vote
1answer
163 views

How to calculate $\int_{|z|=r}\ln(1-z)\,dz$ in dependence of $r\neq1$?

With the integration I mean one counter-clockwise turn around the origin, i.e. $$\int_{\phi=0}^{2\pi}\ln(1-re^{i\phi})ire^{i\phi}d\phi$$ For $r<1$, this is simply a contour integration on a ...