incoherent part of the spectrum. It is obvious that the spectrum we deal with has an lower bound and no upper bound. We can thus expect that coefficients will not converge to some finite values but will grow up to infinity.

In Fig.\[f1\] we represent the coefficients $a_n,b_n$ as functions on $n$ calculated according the procedure described in the preceding section for two values of $J$, $J=0.7\tau $ and $J=0.1\tau $ and for ${\bf k}=\left( \pi
/2,\pi /2\right) $. As it may be seen, the distinctive feature of this dependence is that for large $n$ the coefficients $a_n,b_n$ are linear functions of $n$. For all this, the slope for $a_n$ coefficients is twice as many as the slope for $b_n$. So the coefficients behavior may be approximated as

$$\label{asab}b_n\approx \lambda _1n+\lambda _2,\quad a_n\approx 2\lambda
_1n+\lambda _3,\quad \lambda _i=\lambda _i({\bf k}),\quad n\gg 1$$

It is interesting that the analogous behavior show the coefficients for $t-J$ model approximated by slave-fermion Hamiltonian [@varm] treated within the self-consistent Born approximation [@horsch]. For $J=0.4t,{\bf k}
=\left( \pi /2,\pi /2\right) $ the coefficients $a_n,b_n$ dictated by the relation analogous to (\[gineq1\]) are represented in Fig. \[f2\] (a).

Now we shall show that the same asymptotic (\[asab\]) 