A generalisation of the analytical tetrahedron method is given which allows the evaluation of spectral functions over the entire complex energy plane. Linear interpolation of both the matrix element and the dispersion relations leads to compact and transparent formulae which are free of singularities and well suited for automatic computation. An illustrative calculation is presented of the lattice Green function G(E) for the simple cubic lattice for Im E=0.001 and 0.1.
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Kaprzyk et al. (1986) studied this question.
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