BBP-type formulas -- an elementary approach
Simon Kristensen, Oskar Mathiasen
TL;DR
This paper introduces a simple, flexible method and algorithm for discovering BBP-type formulas, including new formulas for and -based , with an implementation in SageMath.
Contribution
It presents an elementary approach and algorithm for finding BBP-type formulas, including new formulas for and bases, with a versatile SageMath implementation.
Findings
Discovered a new BBP-type formula for .
Found a -based formula in base 1 + .
Successfully implemented a flexible search method in SageMath.
Abstract
We provide a simple way of searching for formulas of the Bailey--Borwein--Plouffe type together with an algorithm and an implementation in \texttt{sage}. Aside from rediscovering some already known formulas, the method has been used in the discovery of a new BBP-type formula for . In addition, the implementation is very flexible and allows us to look for BBP-type formulas to irrational bases but with integer coefficients. As an example of this, searching in various Pisot bases, we have discovered a formula for in base , along with additional formulas.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · Algebraic structures and combinatorial models