A family of criteria for irrationality of Euler's constant
A family of criteria for irrationality of Euler's constant
Following earlier results of Sondow, we propose another criterion of irrationality for Euler's constant $\gamma$. It involves similar linear combinations of logarithm numbers $L\_{n,m}$. To prove that $\gamma$ is irrational, it suffices to prove that, for some fixed $m$, the distance of $d\_n L\_{n,m}$ ($d\_n$ is the least common multiple …