Rational Approximations for Values of Derivatives of the Gamma Function

  title={Rational Approximations for Values of Derivatives of the Gamma Function},
  author={Tanguy Rivoal},
The arithmetical 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 an and bn such that an/bn converges sub-exponentially to γ, viewed as −Γ′(1), where Γ is the usual Gamma function. Although this is not yet enough to prove that γ 6∈ Q, it is major step in this direction. In this paper, we present a… CONTINUE READING

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