Three Series for $1/\pi^2$ and $1/\pi^3$ (Open)
Summary: The proposer identifies three series for reciprocal powers of $\pi$ that are found in fairly recent papers of J. Guillera. Two of the series (each for $1/\pi^2$) have been proved using an ingenious application of the WZ method, while the third series (for $1/\pi^3$) is unproved.
Problem 1. Find non-WZ proofs of the first two series.
Problem 2. Prove the third series.
Classification: Primary, Classical Analysis; Secondary, Sequences and Series
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