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

Kunle Adegoke, Jaume Oliver Lafont and Olawanle Layeni
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 17, 2011, Number 4, Pages 18—32
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Authors and affiliations

Kunle Adegoke
Department of Physics, Obafemi Awolowo University
Ile-Ife, Nigeria

Jaume Oliver Lafont
Conselleria d’Educacio i Cultura, Govern de les Illes Balears
Palma, Spain

Olawanle Layeni
Department of Mathematics, Obafemi Awolowo University
Ile-Ife, Nigeria

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 explicit digit extraction BBPtype formulas in general binary bases b = 212p, for p ∈ Z+ and mod (p, 2) = 1. As particular examples, new binary formulas are presented for π√3, π√3log2, √3Cl2(π/3) and a couple of other polylogaritm constants. A variant of the formula for π√3log2 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.

Keywords

  • BBP-type formulas
  • General binary bases

AMS Classification

  • 11Y60
  • 30B99

References

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  7. Lafont, J. O. Degree 1 BBP-Type Zero Relations. Private communication, available from the author, January 2011.

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Cite this paper

Adegoke, K., Lafont, J. O. & Layeni, O. (2011). A class of digit extraction BBP-type formulas in general binary bases, Notes on Number Theory and Discrete Mathematics, 17(4), 18-32.

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