Euler's factorial series, Hardy integral, and continued fractions

Anne-Maria Ernvall-Hytönen, Tapani Matala-Aho, Louna Seppälä

We study $p$-adic Euler's series $E_p(t)={\sum }_{k=0}^{\infty }k!t^k$ at a point $p^a$, $a\in {\mathbb{Z}}_{\ge 1}$, and use Padé approximations to prove a lower bound for the $p$-ad…