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;0,0,0) or G (1;0,0,0), and π.
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Glasser et al. (2000) studied this question.
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