Exact values for the cubic lattice Green functions

It is shown that the value of the cubic lattice Green functions G(z; l, m, n) at the upper critical point z = 3 (for the simple cubic and face-centred cubic lattices) or z = 1 (for the body-centred cubic lattice) is expressible rationally in terms of the known value of G(3; 0, 0, O) or G(1; 0, 0, 0), and pi.