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Procedures are presented for obtaining the complete low temperature asymptotic behavior of fractional integrals (of Riemann–Liouville type) of squares of Fermi–Dirac integrals. These integrals occur in consideration of the properties of electron systems. The development is presented in the context of calculating the exchange thermodynamic potential for a d-dimensional neutralized homogeneous electron gas interacting via a $1/r$ potential.

Exchange Energy of an Electron Gas of Arbitrary Dimensionality