The following Green’s function for a cubic lattice is evaluated exactly and expressed in terms of the complete elliptic integrals of the first kind: G (E) = (1/π3) ℱℱℱπ0 dxdydz/[E −a1cosx−a2cosy−a3cosz−a2cosycosz−a1 coszcosx].
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F. T. Hioe (1978) studied this question.
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