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arXiv · 1905.12579

Hypergeometric rational approximations to $ζ(4)$

Raffaele Marcovecchio·Wadim Zudilin
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Abstract

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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Raffaele Marcovecchio, Wadim Zudilin. 2019-05-29. Hypergeometric rational approximations to $ζ(4)$. https://doi.org/10.1017/s0013091519000427

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