It's time to calculate

The following identity is an abstract version of the Spitzer's formula introduced in Wendel's 1958 paper [1] and the proof thereof,...

In this post, we will cover a classical but nevertheless powerful result about interchanging the order of limit and sum. Let $G$ be an abe...

Theorem. Let $p, q, r > 0$. If $X \sim \operatorname{Beta}(p, q)$ and $Y \sim \operatorname{Beta}(p+q, r)$, then $$ ...

Consider the problem of finding an antiderivative of $$ \int \frac{1}{a + b \cos x} \, \mathrm{d}x, $$ where $|b| \lt a$. It is o...

In this post, we discuss how certain integrals of rational functions can be computed. Example 1. $$ \int_{0}^{\infty} \frac{x...