The study of 1/n expansions for various atomic matrix elements, where n is the principal quantum number, plays an important role in the theoretical foundations of the quantum defect method. The paper develops an expansion in powers of 1/n² for hydrogenic boundstate wavefunctions which can be used to calculate 1/n expansions of matrix elements. The 1/n expansions of the two-electron direct and exchange Coulomb integrals are evaluated as an example.