On the genesis of BBP formulas
Volume 198 / 2021
Abstract
We present a general procedure to generate infinitely many BBP and BBP-like formulas for the simplest transcendental numbers. This provides some insight into and a better understanding of their nature. In particular, we can derive the main known BBP formulas for $\pi $. We can understand why many of these formulas are rearrangements of each other. We also understand better where some null BBP formulas representing $0$ come from. We also explain what is the observed relation between some BBP formulas for $\log 2$ and $\pi $, which are obtained by taking the real and imaginary parts of a general complex BBP formula. Our methods are elementary, but motivated by transalgebraic considerations, and offer a new way to obtain and to search for many new BBP formulas and, conjecturally, to better understand transalgebraic relations between transcendental constants.
