English

A New Binary BBP-type Formula for $\sqrt 5\,\log\phi$

Number Theory 2016-03-16 v1

Abstract

Hitherto only a base 5 BBP-type formula is known for 5logϕ\sqrt 5\log\phi, where \mbox{ϕ=(5+1)/2\phi=(\sqrt 5+1)/2}, the golden ratio, ( i.e. Formula 83 of the April 2013 edition of Bailey's Compendium of \mbox{BBP-type} formulas). In this paper we derive a new binary BBP-type formula for this constant. The formula is obtained as a particular case of a BBP-type formula for a family of logarithms.

Keywords

Cite

@article{arxiv.1603.04561,
  title  = {A New Binary BBP-type Formula for $\sqrt 5\,\log\phi$},
  author = {Kunle Adegoke},
  journal= {arXiv preprint arXiv:1603.04561},
  year   = {2016}
}
R2 v1 2026-06-22T13:10:57.870Z