We study the ratio of pairs of adjacent correlators of Coulomb-branch operators in SU(2) 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-J behavior on the marginal coupling τ and we find excellent agreement with numerical estimates from localization.