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arXiv · 1603.07395

A class of digit extraction BBP-type formulas in general binary bases

Kunle Adegoke·Jaume Oliver Lafont·Olawanle Layeni
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Abstract

BBP-type formulas are usually discovered experimentally, one at a time and in specific bases, through computer searches. In this paper, however, we derive directly, without doing any searches, explicit digit extraction BBP-type formulas in general binary bases $b=2^{12p}$, for $p$ positive odd integers. As particular examples, new binary formulas are presented for $\pi\sqrt 3$, $\pi\sqrt 3\log 2$, $\sqrt 3\;{\rm Cl}_2(\pi/3)$ and a couple of other polylogarithm constants. A variant of the formula for $\pi\sqrt 3\log 2$ derived in this paper has been known for over ten years but was hitherto unproved. Binary BBP-type formulas for the logarithms of an infinite set of primes and binary BBP-type representations for the arctangents of an infinite set of rational numbers are also presented. Finally, new binary BBP-type zero relations are established.

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Kunle Adegoke, Jaume Oliver Lafont, Olawanle Layeni. 2016-03-23. A class of digit extraction BBP-type formulas in general binary bases. https://arxiv.org/abs/1603.07395

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