Monthly Archives: July 2013

An integral with difficult branch points

The challenge here is merely to evaluate the following integral: $$\int_0^{\infty} dx \frac{\log{(1+x^3)}}{(1+x^2)^2}$$ This integral is a tough one because of the branch points strewn throughout the complex plane, as well as the utter lack of symmetry. It turns out, however, that we may still use the residue theorem to evaluate the integral so long […]

Interesting way to compute $\pi$ and its consequences

A poster on SE wondered how he could prove the following: $$\sum_{j=2}^\infty \prod_{k=1}^j \frac{2 k}{j+k-1} = \pi$$ Well! I never would have thought of this on my own, but I’m not really here to think up stuff like this on my own. Rather, I am here to solve the problems of confused souls, and here […]