A novel approach to the discovery of ternary BBP-type formulas for polylogarithm constants

TL;DR

This paper introduces a new method for deriving ternary BBP-type formulas for polylogarithm constants, proving new formulas and simplifying known results with a clear, direct approach.

Contribution

The paper presents a novel, straightforward technique for discovering ternary BBP-type formulas, including the proof of a previously unproved degree 4 formula and new zero relations.

Findings

Proved new ternary BBP-type formulas for polylogarithm constants.

Revisited and simplified known formulas with a more direct approach.

Established new zero relations confirming known but unproved formulas.

Abstract

Using a clear and straightforward approach, we prove new ternary (base 3) digit extraction BBP-type formulas for polylogarithm constants. Some known results are also rediscovered in a more direct and elegant manner. A previously unproved degree~4 ternary formula is also proved. Finally, a couple of ternary zero relations are established, which prove two known but hitherto unproved formulas.