fact, that the contribution of the terms labelled by the index $\Ba$ in  is negligible at sufficiently large $M$ and $N$, we approximately obtain: $$\begin{aligned}
&\widetilde{\mathcal G}\approx
\biggl[\tr(e^{-{\lambda}{\widehat H}^{0}}{\hat e}_{1,m+1})-
\frac d{d\alpha}\biggr]\det({\hat I}+\widehat{\mathcal M}_1+
\alpha\widehat{\mathcal M}_2)\bigr|_{{\alpha}=0},
\\
&\widehat{\mathcal M}_1+\alpha\widehat{\mathcal M}_2\equiv
e^{-\nu\widehat H^{0}}e^{\widehat S}e^{-\lambda{\widehat H}^{0}}
({\hat I}+\alpha\hat e_{1,m+1}e^{-\lambda{\widehat H}^{0}}),
\end{aligned}
\label{43}$$ where $\hat{ e}_{1,m+1}\equiv
({\delta}_{1,n}{\delta}_{m+1,l})_{1\leq n,l\leq M}$. The matrix $\widehat H^{0}$ is used instead of $\widehat H^{\pm}$ since $s$ can be replaced by zero for the sufficiently large $M$.

The relation  is written in the coordinate representation. In order to pass to the momentum representation it is convenient to use certain formulas provided in [@22]. Keeping the matrix notations as in , we obtain the answer for ${\widetilde F}_{m+1;1}({\lambda})$ (in the limit $M\to\infty$, the corresponding operations should be understood in the sense of the operations over the corresponding integral operators [@26]): $${\widetilde F}_{m+1;1}({\lambda})=
\det({\hat I}+\widehat{\mathcal U}_m)
\biggl[\tr(e^{-{\lambda}\hat{\varepsilon}_{0}}\breve e_{1,m+1})-
\tr\biggl(\frac{\widehat{\mathcal V}_{m}}{{\hat I}+
\widehat{\mathcal U}_m}\biggr)\biggr]
\label{44}$$ (the notation $\tr$, for instance, corresponds to the trace of $M\times M$ matrices). The matrices $\widehat{\mathcal U}_m$, $\widehat{\mathcal V}_{m}$, ${\breve e}_{1,m+1}$ are given by the corresponding momentum representations of the matrices $\widehat{\mathcal M}_1$, $\widehat{\mathcal M}_2$, ${\hat
e}_{1,m+1}$ . However, we shall need explicit expressions only for the 