Rational approximations for values of derivatives of the Gamma function

@article{Rivoal2009RationalAF,
  title={Rational approximations for values of derivatives of the Gamma function},
  author={T. Rivoal},
  journal={Transactions of the American Mathematical Society},
  year={2009},
  volume={361},
  pages={6115-6149}
}
  • T. Rivoal
  • Published 2009
  • Mathematics
  • Transactions of the American Mathematical Society
The arithmetic nature of Euler's constant γ is still unknown and even getting good rational approximations to it is difficult. Recently, Aptekarev managed to find a third order linear recurrence with polynomial coefficients which admits two rational solutions a n and b n such that a n /b n converges sub-exponentially to γ, viewed as ―Γ'(1), where r is the usual Gamma function. Although this is not yet enough to prove that γ ∉ ℚ, it is a major step in this direction. In this paper, we present a… Expand
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