Two hypergeometric tales and a new irrationality measure of $ζ(2)$

preprint2014arXivOpen access

We prove the new upper bound 5.095412 for the irrationality exponent of $ζ(2)=π^2/6$ ; the earlier record bound 5.441243 was established in 1996 by G. Rhin and C. Viola.

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Two hypergeometric tales and a new irrationality measure of $ζ(2)$

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Two hypergeometric tales and a new irrationality measure of ζ(2)ζ(2)ζ(2)

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Two hypergeometric tales and a new irrationality measure of $ζ(2)$