  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 Pad\'e approximants, as advocated in a recent work by Costin and
Dunne, J. Phys. A52, 445205 (2019).
