\begin{eqnarray*}
         \lgg &=&\frac{z}{\bigl({\sigma}_c^{np}+\pee\pge{\sigma}_c^p
                 \bigr)
                 \bigl({\sigma}_c^{np}+\pez\pgz{\sigma}_c^p\bigr)}
                 \Bigl[\Phi_1+\left(\pee\pge+\pez\pgz\right)\Phi_2\\
             &&  +\pee\pge\pez\pgz\Phi_3+\left(\pee\pgse+\pez\pgsz
                 \right)\Phi_4+\left(\pge\pgse+\pgz\pgsz\right)\Phi_5\\
             &&  +\pee\pez\left(\pge\pgsz+\pgse\pgz\right)\Phi_6
                 +\pge\pgz\left(\pee\pgsz+\pgse\pez\right)\Phi_7\\
             &&  +\pgse\pgsz\left(\pee\pgz+\pge\pez\right)\Phi_8
                 +\pee\pgse\pez\pgsz\Phi_9+\pge\pgse\pgz\pgsz\Phi_{10}
                 \Bigr]
\end{eqnarray*}
\medskip
\begin{displaymath}
{\sigma}_c^{np}=\frac{1}{2}+\frac{8}{x}-\frac{1}{2\left(x+1\right)^2}
                +\left(1-\frac{4}{x}-\frac{8}{x^2}\right) \ln\left(x+1\right)
\end{displaymath}
\medskip
\begin{displaymath}
{\sigma}_c^{p}=-\frac{5}{2}+\frac{1}{\left(x+1\right)}-\frac{1}{2\left(x
               +1\right)^2}+\left(1+\frac{2}{x}\right)\ln\left(x+1\right)
\end{displaymath}




