  A formulation of the Green's function method is presented in the n-pole
approximation. Without referring to a specific model we give a general scheme
of calculations that easily permits the computation of the "single-particle"
Green's function in terms of the energy matrix. A theorem is proved which
states that the moments of the spectral density function are conserved up to
the order 2(n-l+1), where l is the order of the composite field. A comparison
with the spectral density approach is also discussed.
