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Display information for equation id:math.2508.4 on revision:2508
* Page found: Reale Gase (eq math.2508.4)
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Hash: e15544dd589c9b208c476544c3ebd80f
TeX (original user input):
\Rightarrow {{e}^{-\Psi }}=Y=\exp \left( \frac{pV}{kT} \right)=\sum\limits_{N=0}^{\infty }{{}}{{\xi }^{N}}\frac{1}{N!}\Phi {{\left( \beta \right)}^{N}}\int_{V}^{{}}{{}}{{d}^{3}}{{q}_{1}}...\int_{V}^{{}}{{}}{{d}^{3}}{{q}_{N}}\exp \left( -\beta \sum\limits_{i<j=1}^{N}{{}}{{\phi }_{ij}} \right)
TeX (checked):
\Rightarrow {{e}^{-\Psi }}=Y=\exp \left({\frac {pV}{kT}}\right)=\sum \limits _{N=0}^{\infty }{}{{\xi }^{N}}{\frac {1}{N!}}\Phi {{\left(\beta \right)}^{N}}\int _{V}^{}{}{{d}^{3}}{{q}_{1}}...\int _{V}^{}{}{{d}^{3}}{{q}_{N}}\exp \left(-\beta \sum \limits _{i<j=1}^{N}{}{{\phi }_{ij}}\right)
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MathML (2.676 KB / 507 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>⇒</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mi mathvariant="normal">Ψ</mi></mrow></mrow></msup><mo>=</mo><mi>Y</mi><mo>=</mo><mi>exp</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>p</mi><mi>V</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mi>T</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>N</mi><mo>=</mo><mn>0</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><msup><mi>ξ</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msup><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><mi>exp</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>−</mo><mi>β</mi><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><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></munderover><msub><mi>ϕ</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></mstyle></mrow></math>
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