Numerical approximation to ζ(2n+1)

Tian-Xiao He, Michael J. Dancs

Research output: Journal ArticleArticlepeer-review

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.

Original languageAmerican English
JournalJournal of Computational and Applied Mathematics
Volume196
StatePublished - 2006

Keywords

  • Riemann zeta function
  • Bernoulli polynomial
  • Dirichlet series
  • Apery’s constant.

Disciplines

  • Applied Mathematics
  • Mathematics

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