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

Kunle Adegoke
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 17, 2011, Number 1, Pages 4–20
Full paper (PDF, 207 Kb)

Details

Authors and affiliations

Kunle Adegoke
Department of Physics, Obafemi Awolowo University
Ile-Ife, Nigeria

Abstract

Using clear and straightforward approaches, 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. An hitherto 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.

Keywords

• Integral quadratic form
• Nonsingular quadratic form
• Diagonalization quadratic form modulo prime

AMS Classification

• 11Y60
• 30B99

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