Numerical approximation to ζ(2n+1)

摘要

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.