k},z)$, and the coefficients $\tilde a_n,\tilde b
_n,n\leq n_0$, and then substitute it for $T_{n_0}({\bf k},z)$ (see [@t1] for the details of matching Greenians).

We thus obtain $G({\bf k},z)$ in the whole complex energy plane including the real axis. Note that usually the procedure of discretizing the energy range $\omega $ is used for iteration process when the Dyson’s equation is solved numerically. It is not obvious that such a self-consistent solution leads to the correct analytical properties of the resulting Green’s function. In contrast the continued fraction representation guarantees these properties (e.g. the positive definiteness of spectral function $A_p({\bf k}
,\omega )$).

Results and discussion
======================

In this section we represent our results for the retarded Green’s function $
G({\bf k},\omega )$ for three-band model at $T=0$. The self consistent equation (\[gineq\]) was solved on a $32\times 32$ cell lattice. The number of calculated CF levels $n_0$ was taken $n_0=30$.

To begin with, we check the validity of the method outlined above by calculating the spinless hole Green’s function for the $t-J$ model and compare the results with the results of Martinez and Horsch [@horsch] obtained by usual iteration procedure. In Fig.\[f2\] $A_h({\bf k}_1,\omega +\imath \eta ),{\rm Re}\Sigma 
({\bf 