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
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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

References

  1. David H. Bailey, Peter B. Borwein, and Simon Plou_e. On the rapid computation of various polylogarithmic constants. Mathematics of Computation, 66(218):903-913, 1997.
  2. D. H. Bailey. A compendium of bbp-type formulas for mathematical constants http://crd.lbl.gov/~dhbailey/dhbpapers/bbp-formulas.pdf. October 2010.
  3. David H. Bailey and Richard E. Crandall. On the random character of fundamental constant expansions. Experimental Mathematics, 10:175, 2001.
  4. Jonathan M. Borwein, David Borwein, and William F. Galway. Finding and excluding b-ary machin-type BBP formulae. Available Online http://crd.lbl.gov/~dhbailey/ dhbpapers/machin.pdf , 2002.
  5. Marc Chamberland. Binary bbp-formulae for logarithms and generalized gaussian- mersenne primes. Journal of Integer Sequences, 6, 2003.
  6. Leonard Lewin. Polylogarithms and associated functions. Elsevier North Holland Inc., 1981.
  7. Kunle Adegoke. A non-pslq route to bbp-type formulas. Journ. Maths. Res., 2:56-64, 2010.
  8. Kunle Adegoke. New binary and ternary digit extraction (bbp-type) formulas for trilog- arithm constants. New York J. Math., 16:361-367, 2010.
  9. David J. Broadhurst. Massive 3-loop Feynman Diagrams Reducible to SC* Primitives of algebras of the sixth root of unity. Available Online http://xxx.lanl.gov/format/hep-ph/9803091 , 1998.
  10. D. J. Broadhurst. Polylogarithmic ladders, hypergeometric series and the ten millionth digits of ζ(3) and ζ(5). arXiv:math/9803067v1 [math.CA], 1998.

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Cite this paper

APA

Adegoke, K. (2011). A novel approach to the discovery of ternary BBP-type formulas for polylogarithm constants, Notes on Number Theory and Discrete Mathematics, 17(1), 4-20.

Chicago

Adegoke, Kunle. “A Novel Approach to the Discovery of Ternary BBP-type Formulas for Polylogarithm Constants.” Notes on Number Theory and Discrete Mathematics 17, no. 1 (2011): 4-20.

MLA

Adegoke, Kunle. “A Novel Approach to the Discovery of Ternary BBP-type Formulas for Polylogarithm Constants.” Notes on Number Theory and Discrete Mathematics 17.1 (2011): 4-20. Print.

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