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Display information for equation id:math.2517.38 on revision:2517
* Page found: Klassisch- mechanische Gleichgewichtsverteilungen (eq math.2517.38)
(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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MathML (2.38 KB / 502 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="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>N</mi><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><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mi>N</mi></mtd></mtr><mtr><mtd></mtd><mtd><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</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></munderover></mstyle><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>=</mo><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo>=</mo><msup><mi>Y</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</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><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</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></munderover></mstyle><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>−</mo><mi>β</mi><mi>H</mi></mrow></mrow></msup></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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