  We describe the Adler function in Quantum Chromodynamics using a transseries
representation within a resurgent framework. The approach is based on a
Borel-Ecalle resummation of the infrared renormalons combined with an effective
running for the strong coupling. The new approach is flexible enough to give
values in agreement with the current Adler function determinations. We then
apply our finding to the muon's anomalous magnetic moment studying the
possibility of saturating, solely in terms of the vacuum polarization function,
the current discrepancy between the best Standard Model value for the muon's
anomalous magnetic moment and the experimental value obtained by the most
recent muon g-2 collaboration. The latter shows that the Adler function's new
representation can also be consistent with recent lattice determinations.
