잡담을 위한 소박한 장소

Today's integral is so called Abel's integral, which is given by Problem. \begin{equation} \label{eq:prob} \int_{0}^{\infty} \frac{t \; dt}{(e^{\pi t} - e^{-\pi t})(t^2 + 1)} \end{equation} Now our aim is to evaluate \eqref{eq:prob} in closed form. We preliminarily introduce a function that will play a key role throughout the calculation. Let $k$ be a nonnegative integer. Then we define polygamm..