Once you guess the formula, the proof is just a few lines of calculus. It's accessible to anyone who has taken Calc I, I think. The full text .pdf of the original paper [0] is freely available; the result is Theorem 1, whose proof is on pages 2 and 3.
I believe the formula was found by computer search, but my memory could be failing me. The three people the result is named after are all well-known for computer-assisted mathematics, for instance using the PSLQ algorithm [1].
