  We study the ratio of pairs of adjacent correlators of Coulomb-branch
operators in $SU(2)$ $\mathcal{N}=2$ SQCD with four flavors within the
framework of the Large Quantum Number Expansion. Capitalizing on the
order-by-order S-duality invariance of the large-R-charge expansion we compute
ab initio the dependence of the leading large-$\mathcal{J}$ behavior on the
marginal coupling $\tau$ and we find excellent agreement with numerical
estimates from localization.
