The computation of previously inaccessible digits of π2 and Catalan’s constant (2013)

  • David H. Bailey
  • Jonathan M. Borwein
  • Andrew Mattingly
  • Glenn Wightwick


Paper 20: David H. Bailey, Jonathan M. Borwein, Andrew Mattingly and Glenn Wightwick, “The computation of previously inaccessible digits of π 2 and Catalan’s constant,” Notices of the American Mathematical Society, vol. 60 (2013), p. 844–854. Reprinted by permission of the American Mathematical Society.

Synopsis: An earlier selection (paper #14 in this collection) presented what is now known as the BBP formula for π, which permits one to calculate binary or base-16 digits of π beginning at an arbitrary starting point. The original BBP paper presented a similar formula for π 2, permitting arbitrary binary digits of π 2 to be calculated by this same general process. Since the publication of that paper, additional BBP-type formulas have also been found, among them one that permits arbitrary base-3 digits of π 2 to be calculated, and another that permits arbitrary binary digits of Catalan’s constant = \( {\displaystyle {\sum}_{n=0}^{\infty }{\left(-1\right)}^n/{\left(2n+1\right)}^2} = 0.9159965594… \) to be calculated.


Computation History Normality General Audience 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • David H. Bailey
    • 1
  • Jonathan M. Borwein
    • 2
  • Andrew Mattingly
    • 3
  • Glenn Wightwick
    • 3
  1. 1.Lawrence Berkeley National LaboratoryBerkeleyUSA
  2. 2.University of NewcastleNewcastleAustralia
  3. 3.IBM AustraliaSydneyAustralia

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