For the ground state configuration the first terms (the integrals) of the expressions above yield the internal energy and electron density of the ground state. The expression for the electron density reduces to ( μ μ − − ϵ ϵ f ) D ( ϵ ϵ f ) + π π 2 6 ( k B T ) 2 D ˙ ˙ ( ϵ ϵ f ) = 0 . Substituting this into the expression for the internal energy, one finds the following expression: