Numerical approximation to ζ(2n + 1)

  • Authors:

  • Michael J. Dancs;Tian-Xiao He

  • Affiliations:

  • Department of Mathematics and Computer Science, Illinois Wesleyan University, Bloomington, IL;Department of Mathematics and Computer Science, Illinois Wesleyan University, Bloomington, IL

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2006

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Abstract

In this short paper, we establish a family of rapidly converging series expansions for ζ(2n + 1) by discretizing an integral representation given by Cvijović 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.