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arXiv · 1906.09629

On the genesis of BBP formulas

Daniel Barsky·Vicente Muñoz·Ricardo Pérez-Marco
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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.

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Daniel Barsky, Vicente Muñoz, Ricardo Pérez-Marco. 2019-06-23. On the genesis of BBP formulas. https://doi.org/10.4064/aa200619-28-9

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