  Falicov and Kimball proposed a real-axis form for the free energy of the
Falicov-Kimball model that was modified for the coherent potential
approximation by Plischke. Brandt and Mielsch proposed an imaginary-axis form
for the free energy of the dynamical mean field theory solution of the
Falicov-Kimball model. It has long been known that these two formulae are
numerically equal to each other; an explicit derivation showing this
equivalence is presented here.
