This repository contains some Mathematica notebooks for the calculation of the resurgent transeries of the quantum mechanical quartic double-well potential. Also, there are the asymptotic expansion of a few special functions from Mathematical Physics, like the Zeta function and the Beta function.
Physical observables like the energy spectrum and the scattering amplitude are given by a perturbative power series. This kind of series generally diverges for every non-zero value of the coupling constant, although keeping only a few terms provides well agreement with experimental data. The explanation to this issue comes from the theory of the resurgent transseries, which describes non-perturbative expansions generated by asymptotically divergent series. For a comprehensible guide to the subject see the file 2-Resurgent Transseries.pdf or go to https://arxiv.org/abs/1802.10441