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arXiv:1204.4162 [math.CO]AbstractReferencesReviewsResources

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

Yijun Chen

Published 2012-04-18, updated 2012-07-30Version 2

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.

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
Categories: math.CO, math.CA, math.HO
Subjects: 05A19
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