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Display information for equation id:math.2520.38 on revision:2520
* Page found: Klassisch- mechanische Gleichgewichtsverteilungen (eq math.2520.38)
(force rerendering)Occurrences on the following pages:
Hash: d6e61e42ebb0fb8f7448c73919ce2ef6
TeX (original user input):
\begin{align}
& \left\langle N \right\rangle =\sum\limits_{N=0}^{\infty }{{}}{{P}_{N}}N \\
& \int_{{{R}^{6N}}}^{{}}{{}}d{{\xi }_{N}}\rho \left( {{\xi }_{N}} \right)={{P}_{N}}={{Y}^{-1}}{{e}^{\beta \mu N}}\int_{{{R}^{6N}}}^{{}}{{}}d{{\xi }_{N}}{{e}^{-\beta H}} \\
\end{align}
TeX (checked):
{\begin{aligned}&\left\langle N\right\rangle =\sum \limits _{N=0}^{\infty }{}{{P}_{N}}N\\&\int _{{R}^{6N}}^{}{}d{{\xi }_{N}}\rho \left({{\xi }_{N}}\right)={{P}_{N}}={{Y}^{-1}}{{e}^{\beta \mu N}}\int _{{R}^{6N}}^{}{}d{{\xi }_{N}}{{e}^{-\beta H}}\\\end{aligned}}
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<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>N</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">=</mo><munderover><mo form="prefix" movablelimits="false" stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>N</mi><mo stretchy="false">=</mo><mn>0</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mi>N</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>6</mn><mi>N</mi></mrow></mrow></msup></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><mi>d</mi><msub><mi>ξ</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mi>ρ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>ξ</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo stretchy="false">=</mo><msup><mi>Y</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mn>1</mn></mrow></mrow></msup><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>β</mi><mi>μ</mi><mi>N</mi></mrow></mrow></msup><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>6</mn><mi>N</mi></mrow></mrow></msup></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><mi>d</mi><msub><mi>ξ</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mi>β</mi><mi>H</mi></mrow></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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