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

preprint2012arXivOpen access

Abstract

Based on the framework of the WZ theory, a new evaluation for ς(2)=π26ς(2) = \frac{π^2}{6} and ς(4)=π490ς(4) = \frac{π^4}{90} was given respectively, finally, a new recurrence formula for ς(2k)ς(2k) was given.

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