Article
Numerical approximation to ζ(2n+1)
Journal of Computational and Applied Mathematics
(2006)
Abstract
In this short paper, we establish a family of rapidly converging series expansions ζ(2n +1) by discretizing an integral representation given by Cvijovic and Klinowski [3] in Integral representations of the Riemann zeta function for odd-integer arguments, J. Comput. Appl. Math. 142 (2002) 435–439. The proofs are elementary, using basic properties of the Bernoulli polynomials.
Keywords
- Riemann zeta function,
- Bernoulli polynomial,
- Dirichlet series,
- Apery’s constant.
Disciplines
Publication Date
2006
Publisher Statement
The Journal of Computational and Applied Mathematics is published by Elsevier, http://www.journals.elsevier.com/journal-of-computational-and-applied-mathematics/.
Citation Information
Tian-Xiao He and Michael J. Dancs. "Numerical approximation to ζ(2n+1)" Journal of Computational and Applied Mathematics Vol. 196 (2006) Available at: http://works.bepress.com/tian_xiao_he/26/