A Compendium of BBP-Type Formulas for Mathematical Constants

Abstract

A 1996 paper by the author, Peter Borwein and Simon Plouffe showed that any mathematical constant given by an infinite series of a certain type has the property that its n-th digit in a particular number base could be calculated directly, without needing to compute any of the first n−1 digits, by means of a simple algorithm that does not require multiple-precision arithmetic. Several such formulas were presented in that paper, including formulas for the constants π and log 2. Since then, numerous other formulas of this type have been found. This paper presents a compendium of currently known results of this sort, both formal and experimental. Many of these results were found in the process of compiling this collection and have not previously appeared in the literature. Several conjectures suggested by these results are mentioned.