Variations on the Resurgence of the Gamma Function

TL;DR

This paper reviews Ecalle's formalism and provides explicit formulas demonstrating the resurgence of the exponential of the Stirling series, analyzing its Stokes phenomena through alien calculus.

Contribution

It introduces explicit formulas in the Borel plane for the resurgence of the exponential of the Stirling series and discusses Stokes phenomena using alien calculus.

Findings

Explicit formulas for resurgence in the Borel plane.

Analysis of Stokes phenomena via alien calculus.

Connection between Ecalle's formalism and resurgence theory.

Abstract

We review \'Ecalle's formalism of minors, natural-majors and real-majors, and provide explicit formulas in the Borel plane that show the resurgence of the exponential of the Stirling series. We also discuss its Stokes phenomena in the framework of alien calculus.