잡담을 위한 소박한 장소

While calculating a specific problem, I succeeded in proving a more general problem. Proposition. For $0 < r < 1$ and $r < s$, the following holds:[1] \begin{equation} \label{eq_wts} \int_{-1}^{1} \frac{1}{x} \sqrt{\frac{1+x}{1-x}} \log \left| \frac{1 + 2rsx + (r^{2} + s^{2} - 1)x^{2}}{1 - 2rsx + (r^{2} + s^{2} - 1)x^{2}} \right| \, dx = 4\pi \arcsin r. \end{equation} Proof. We divide the proof ..