$ K =\displaystyle\frac{1}{2 m }\sum_ i ^ N \vec{p} _ i ^2$

K =@SUM( &p_i ^2/(2* m ), i , 1 , N )

$U=\displaystyle\frac{1}{2}\sum_{i,j,i\neq j}u_{ij}$

U=\displaystyle\frac{1}{2}\sum_{i,j,i\neq j}u_{ij}

$ u(r) =4 u_0 \left[\left(\displaystyle\frac{ a }{ r }\right)^{12}-\left(\displaystyle\frac{ a }{ r }\right)^6\right]$

u_r =4* u_0 *[( a / r )^12 -( a / r )^6]

$ \ln Z_U = N \ln V -\displaystyle\int_0^{ \beta } \bar{U}( \beta_h )d \beta_h $

lnZ_U = N *ln( V )- @INTEGRATE( U , beta_h , 0 , beta )

$\bar{U}=\displaystyle\frac{1}{2}N^2\bar{u}$

\bar{U}=\displaystyle\frac{1}{2}N^2\bar{u}

$\bar{U}=-\displaystyle\frac{1}{2}\displaystyle\frac{N^2}{V}\displaystyle\frac{\partial I}{\partial\beta}$

\bar{U}=-\displaystyle\frac{1}{2}\displaystyle\frac{N^2}{V}\displaystyle\frac{\partial I}{\partial\beta}

$\bar{u}=-\displaystyle\frac{1}{V}\displaystyle\frac{\partial I}{\partial\beta}$

\bar{u}=-\displaystyle\frac{1}{V}\displaystyle\frac{\partial I}{\partial\beta}