Schwinger pair production from Pade-Borel reconstruction

In this work, we show how the knowledge of the first few terms of the Euler-Heisenberg Lagrangian's weak-field expansion in a magnetic field background is enough to reconstruct the pair-production rate in a strong electric field background. To this end, we study its associated truncated Borel sum using Pade approximants, as advocated in a recent work by Costin and Dunne [10].