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

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.

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

Cited by in corpus (1)

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