# On the genesis of BBP formulas

## TL;DR

This paper introduces a general, elementary method for generating and understanding BBP and BBP-like formulas for transcendental numbers, shedding light on their structure, relations, and origins.

## Contribution

It provides a new elementary procedure to produce infinitely many BBP formulas, explaining their interrelations and origins, especially for $ ext{pi}$ and logarithmic constants.

## Key findings

- Derived known BBP formulas for $ ext{pi}$
- Explained relations and rearrangements among BBP formulas
- Identified sources of null BBP formulas for zero

## Abstract

We present a general procedure to generate infinitely many BBP and BBP-like formulas for the simplest transcendental numbers. This provides some insight and a better understanding into 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 $\pi$, that are obtained by taking 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 many new BBP formulas and, conjecturally, to better understand transalgebraic relations between transcendental constants.