On Catalan’S constant

  title={On Catalan’S constant},
  author={Y. Nesterenko},
  journal={Proceedings of the Steklov Institute of Mathematics},
  • Y. Nesterenko
  • Published 2016
  • Mathematics
  • Proceedings of the Steklov Institute of Mathematics
A new efficient construction of Diophantine approximations to Catalan’s constant is presented that is based on the direct analysis of the representation of a hypergeometric function with specially chosen half-integer parameters as a series and as a double Euler integral over the unit cube. This allows one to significantly simplify the proofs of Diophantine results available in this domain and substantially extend the capabilities of the method. The sequences of constructed rational… Expand