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\begin{document} $$ - E = \frac{1}{2} \sum_{i=1}^{N} \sum_{j=i_1}^{i_N} \phi_{ij} \left\( r_{ij} \right\) - \sum_{i=1}^{N} \sum_{j=i_1}^{i_N} \beta_{\sigma,ij} \left\( r_{ij} \right\) \cdot \Theta_{\sigma,ij} - \sum_{i=1}^{N} \sum_{j=i_1}^{i_N} \beta_{\pi,ij} \left\( r_{ij} \right\) \cdot \Theta_{\pi,ij} + U_{prom} + E = \frac{1}{2} \sum_{i=1}^{N} \sum_{j=i_1}^{i_N} \phi_{ij} \left( r_{ij} \right) - \sum_{i=1}^{N} \sum_{j=i_1}^{i_N} \beta_{\sigma,ij} \left( r_{ij} \right) \cdot \Theta_{\sigma,ij} - \sum_{i=1}^{N} \sum_{j=i_1}^{i_N} \beta_{\pi,ij} \left( r_{ij} \right) \cdot \Theta_{\pi,ij} + U_{prom} $$ \end{document}