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Display information for equation id:math.2508.13 on revision:2508
* Page found: Reale Gase (eq math.2508.13)
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Hash: 9f443bbf22b624a37ed17132ded5ba16
TeX (original user input):
\begin{align}
& \int_{{{R}^{3}}}^{{}}{{}}{{f}_{ij}}(r){{d}^{3}}r=\int_{0}^{\infty }{{}}\left( {{e}^{-\beta \phi (r)}}-1 \right)4\pi {{r}^{2}}dr \\
& =\left. \left( {{e}^{-\beta \phi (r)}}-1 \right)\frac{4\pi }{3}{{r}^{3}} \right|_{0}^{\infty }+\frac{4\pi \beta }{3}\int_{0}^{\infty }{{}}\left( \frac{\partial \phi }{\partial r}r \right){{e}^{-\beta \phi (r)}}{{r}^{2}}dr \\
\end{align}
TeX (checked):
{\begin{aligned}&\int _{{R}^{3}}^{}{}{{f}_{ij}}(r){{d}^{3}}r=\int _{0}^{\infty }{}\left({{e}^{-\beta \phi (r)}}-1\right)4\pi {{r}^{2}}dr\\&=\left.\left({{e}^{-\beta \phi (r)}}-1\right){\frac {4\pi }{3}}{{r}^{3}}\right|_{0}^{\infty }+{\frac {4\pi \beta }{3}}\int _{0}^{\infty }{}\left({\frac {\partial \phi }{\partial r}}r\right){{e}^{-\beta \phi (r)}}{{r}^{2}}dr\\\end{aligned}}
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