Rational approximations for values of derivatives of the Gamma function
Rational approximations for values of derivatives of the Gamma function
The arithmetic nature of Euler’s constant $\gamma$ 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 $\gamma$, viewed as …