Evaluations for zeta(2),zeta(4),...,zeta(2k)based on the WZ method

Yijun Chen

Evaluations for zeta(2),zeta(4),...,zeta(2k)based on the WZ method

Combinatorics 2012-08-01 v2 Classical Analysis and ODEs History and Overview

Authors: Yijun Chen

Abstract

Based on the framework of the WZ theory, a new evaluation for $\varsigma (2) = \frac{\pi ^2}{6}$ and $\varsigma (4) = \frac{\pi ^4}{90}$ was given respectively, finally, a new recurrence formula for $\varsigma (2k)$ was given.

Keywords

zeta function WZ method recurrence formula evaluation Riemann zeta values

Cite

@article{arxiv.1204.4162,
  title  = {Evaluations for zeta(2),zeta(4),...,zeta(2k)based on the WZ method},
  author = {Yijun Chen},
  journal= {arXiv preprint arXiv:1204.4162},
  year   = {2012}
}

Comments

9 pages; some comments given by Vignat Christophe to me were added to this vesion, best thanks to Vignat Christophe; the proof of lemma 5 was improved; some misprints were corrected

Evaluations for zeta(2),zeta(4),...,zeta(2k)based on the WZ method

Abstract

Keywords

Cite

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