Euler's factorial series and global relations

Abstract

Using Padé approximations to the series $E(z)={\sum }_{k=0}^{\infty }k!(-z{)}^k$, we address arithmetic and analytical questions related to its values in both $p$-adic and Archimedean valuations.

arXiv comment9 pages

References in corpus (3)

• Euler's constant: Euler's work and modern developments
• De seriebus divergentibus
• A determinantal approach to irrationality