Exchange density-functional gradient expansion

The coefficient ₗ of the first term in a gradient expansion of the Hartree-Fock (HF) density functional was calculated by Sham to first order in e^2. It is now known that ₗ^HF diverges if e^2 is included to all orders. It has recently been claimed that if the exchange energy is defined in terms of density-functional (DF) eigenfunctions, rather than HF eigenfunctions, not only is ₗ^DF first order in e^2 but also ₗ^DF=ₒ₇₀₌. It is proven in this paper that, in fact, ₗ^DF=87ₒ₇₀₌.