This paper analytically solves the "inverse DFT problem" of mapping the ground-state density to the exact XC functional. And the exact density, i.e. the FCC/FCI density, can be expressed as an infinite series of basis sets with transcendentally analytically expressable coefficients(all one-variable polynomial equations are known to be solvable in analytic form using transcendental functions). This means that the exact XC functional can be expressed as an infinite series of analytically expressable terms.
My question now follows- is there any known way to find out any "cancellations" in the expansion before (truncating it to yield approximations)?