A class of digit extraction BBP-type formulas in general binary bases
| Autor: | Adegoke, Kunle, Lafont, Jaume Oliver, Layeni, Olawanle |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Notes on Number Theory and Discrete Mathematics (2011) 17 (4): 18-32 |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: arXiv admin note: text overlap with arXiv:1603.05810 |
| Databáze: | arXiv |
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