Convergence Analysis of the Summation of the Euler Series by Pad\'e Approximants and the Delta Transformation

Understand

Sequence transformations are valuable numerical tools that have been used with considerable success for the acceleration of convergence and the summation of diverging series.

• However, our understanding of their theoretical properties is far from satisfactory.
• The Euler series $\mathcal{E}(z) \sim \sum_{n=0}^{\infty} (-1)^n n! z^n$ is a very important model for the ubiquitous factorially divergent perturbation expansions in physics.
• In this article, we analyze the summation of the Euler series by Pad\'e approximants and the delta transformation [E.