$n$ dipoles and we consider the emission of the $n$th gluon, we will get a contribution $$\sum_{ij}\int d^2\bold{x}_n\frac{x_{ij}^2}{x_{in}^2x_{nj}^2}$$ where $ij$ runs over all the indices for which there exist a dipole.

(400,200)(0,0) (100,60)(100,140) (100,140)(140,160) (100,60)(140,160) (100,60)(160,40) (140,160)(160,40) (100,140)[2]{} (100,60)[2]{} (140,160)[2]{} (160,40)[2]{} (140,160)(180,175) (180,175)(160,40) (180,175)[2]{} (100,150)\[\][$0$]{} (100,50)\[\][$1$]{} (140,170)\[\][$2$]{} (165,40)\[\][$3$]{} (190,175)\[\][$4$]{} (185,116)\[\][$\bold{\cdots}$]{}

The complete formula for the wave function with arbitrarily many gluons is derived from a generating functional. Mueller derived a non-linear integral equation for this generating functional. Taking into account not only real gluon emissions, but also the leading logarithmic virtual corrections, the formula reads $$\begin{aligned}
Z(\bold{b}_0,\bold{x}_{10},Y,u)&=&u(\bold{b}_0,\bold{x}_{10})exp\biggl[-2\bar{\alpha}\textrm{ln}\biggl(\frac{x_{10}}{\rho}\biggr)Y\biggr]+
\nonumber \\
& & +\frac{\bar{\alpha}}{2\pi}\int_0^Y dyexp\biggl[-2\bar{\alpha}\textrm{ln}\biggl(\frac{x_{10}}{\rho}\biggr)(Y-y)\biggr] \times \label{eq:mueller} \\
& & \times \int_\rho d^2\bold{x}_2\frac{x_{10}^2}{x_{20}^2x_{12}^2}Z(\bold{b}_0
  +\frac{1}{2}\bold{x}_{12},\bold{x}_{20},y,u)Z(\bold{b}_0
  -\frac{1}{2}\bold{x}_{20},\bold{x}_{12},y,u)
\nonumber \end{aligned}$$ Here the $\rho$ under the second integral indicates that we are integrating over a region satisfying, $x_{20}\geqslant \rho$ and $x_{21}\geqslant
\rho$. The vector $\bold{b}_0$ is the position of the center of the initial dipole in transverse coordinates. The two exponentials have the meaning of Sudakov factors, where in the first one we consider the probability that nothing happens within the allowed rapidity interval, which means that there are no gluons present. The second exponential contains the probability that nothing happens after the last gluon is 