  We devise a prescription to utilize a novel convergent expansion in the
strong-asymptotic regime for the Stieltjes integral and its generalizations
[Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to sum the associated divergent
series of Stieltjes across all asymptotic regimes. The novel expansion makes
use of the divergent negative-power moments which we treated as Hadamard's
finite part integrals. The result allowed us to compute the ground-state energy
of the quartic, sextic anharmonic oscillators as well as the $\mathcal{PT}$
symmetric cubic oscillator, and the funnel potential across all perturbation
regimes from a single expansion that is built from the divergent weak-coupling
perturbation series and incorporates the known leading-order strong-coupling
behavior of the spectra.
