Hypergeometry inspired by irrationality questions

@article{Krattenthaler2018HypergeometryIB,
  title={Hypergeometry inspired by irrationality questions},
  author={C. Krattenthaler and W. Zudilin},
  journal={arXiv: Number Theory},
  year={2018}
}
We report new hypergeometric constructions of rational approximations to Catalan's constant, $\log2$, and $\pi^2$, their connection with already known ones, and underlying `permutation group' structures. Our principal arithmetic achievement is a new partial irrationality result for the values of Riemann's zeta function at odd integers. 
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TLDR
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