Hypergeometric rational approximations to $ζ(4)$

We give a new hypergeometric construction of rational approximations to $ζ(4)$, which absorbs the earlier one from 2003 based on Bailey's ${}_9F_8$ hypergeometric integrals. With the novel ingredients we are able to get a better control of arithmetic and produce a record irrationality measure for $ζ(4)$.

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