Numerical approximation to ζ(2n+1)
- 作者：Michael J. Dancs and Tian-Xiao He
- 关键词：Riemann zeta function ; Bernoulli polynomial ; Dirichlet series ; Apé ; ry's constant
- 刊名：Journal of Computational and Applied Mathematics
- 出版年：2006
- 期刊代码：72_03770427
- 类别：cp
- 出版时间：1 November 2006
- 卷：196
- 期：1
- 页码：150-154
- 文件大小：145 K
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.