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Display information for equation id:math.2508.10 on revision:2508
* Page found: Reale Gase (eq math.2508.10)
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Hash: 0d69ee022fd8e195499f3cfb79642e21
TeX (original user input):
\begin{align}
& \frac{1}{N!}\Phi {{\left( \beta \right)}^{N}}\int_{V}^{{}}{{}}{{d}^{3}}{{q}_{1}}...\int_{V}^{{}}{{}}{{d}^{3}}{{q}_{N}}\prod\limits_{i<j}^{{}}{{}}\left( 1+{{f}_{ij}} \right) \\
& \approx \frac{1}{N!}\Phi {{\left( \beta \right)}^{N}}\int_{V}^{{}}{{}}{{d}^{3}}{{q}_{1}}...\int_{V}^{{}}{{}}{{d}^{3}}{{q}_{N}}\left( 1+\sum\limits_{i<j}^{{}}{{}}{{f}_{ij}}+\sum\limits_{\begin{smallmatrix}
i<j \\
k<l
\end{smallmatrix}}^{{}}{{}}{{f}_{ij}}{{f}_{kl}}+.... \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&{\frac {1}{N!}}\Phi {{\left(\beta \right)}^{N}}\int _{V}^{}{}{{d}^{3}}{{q}_{1}}...\int _{V}^{}{}{{d}^{3}}{{q}_{N}}\prod \limits _{i<j}^{}{}\left(1+{{f}_{ij}}\right)\\&\approx {\frac {1}{N!}}\Phi {{\left(\beta \right)}^{N}}\int _{V}^{}{}{{d}^{3}}{{q}_{1}}...\int _{V}^{}{}{{d}^{3}}{{q}_{N}}\left(1+\sum \limits _{i<j}^{}{}{{f}_{ij}}+\sum \limits _{\begin{smallmatrix}i<j\\k<l\end{smallmatrix}}^{}{}{{f}_{ij}}{{f}_{kl}}+....\right)\\\end{aligned}}
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MathML (4.229 KB / 572 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>N</mi><mi>!</mi></mrow></mrow></mfrac></mrow><mi mathvariant="normal">Φ</mi><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>β</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msup><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>.</mo><mo>.</mo><mo>.</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><munderover><mo form="prefix" texclass="OP">∏</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo><</mo><mi>j</mi></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo>+</mo><msub><mi>f</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>j</mi></mrow></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>≈</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>N</mi><mi>!</mi></mrow></mrow></mfrac></mrow><mi mathvariant="normal">Φ</mi><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>β</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msup><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>.</mo><mo>.</mo><mo>.</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo>+</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo><</mo><mi>j</mi></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><msub><mi>f</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>j</mi></mrow></mrow></msub><mo>+</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN"></mo><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mi>i</mi><mo><</mo><mi>j</mi></mtd></mtr><mtr><mtd><mi>k</mi><mo><</mo><mi>l</mi></mtd></mtr></mtable></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><msub><mi>f</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>j</mi></mrow></mrow></msub><msub><mi>f</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mi>l</mi></mrow></mrow></msub><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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