Zur Navigation springen
Zur Suche springen
General
Display information for equation id:math.2573.12 on revision:2573
* Page found: Spezifische Wärme zweiatomiger idealer Gase (eq math.2573.12)
(force rerendering)Occurrences on the following pages:
Hash: 6fa33c321cfa3af9c878c1d37849ae1e
TeX (original user input):
\begin{align}
& Z=\frac{1}{N!}{{Z}^{N}}=\frac{1}{N!}{{\left( \sum\limits_{t,r,s}^{{}}{{}}\exp \left( -\beta {{E}_{j}} \right) \right)}^{N}}=\frac{1}{N!}{{Z}_{t}}^{N}{{Z}_{r}}^{N}{{Z}_{S}}^{N} \\
& =\frac{1}{N!}\sum\limits_{t}^{{}}{{}}\exp \left( -N\beta {{E}_{t}} \right)\sum\limits_{r}^{{}}{{}}\exp \left( -N\beta {{E}_{r}} \right)\sum\limits_{s}^{{}}{{}}\exp \left( -N\beta {{E}_{s}} \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&Z={\frac {1}{N!}}{{Z}^{N}}={\frac {1}{N!}}{{\left(\sum \limits _{t,r,s}^{}{}\exp \left(-\beta {{E}_{j}}\right)\right)}^{N}}={\frac {1}{N!}}{{Z}_{t}}^{N}{{Z}_{r}}^{N}{{Z}_{S}}^{N}\\&={\frac {1}{N!}}\sum \limits _{t}^{}{}\exp \left(-N\beta {{E}_{t}}\right)\sum \limits _{r}^{}{}\exp \left(-N\beta {{E}_{r}}\right)\sum \limits _{s}^{}{}\exp \left(-N\beta {{E}_{s}}\right)\\\end{aligned}}
LaTeXML (experimentell; verwendet MathML) rendering
MathML (0 B / 8 B) :
SVG image empty. Force Re-Rendering
SVG (0 B / 8 B) :
MathML (experimentell; keine Bilder) rendering
MathML (3.552 KB / 494 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><mi>Z</mi><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><msup><mi>Z</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msup><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><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>t</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>s</mi></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mi>exp</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>−</mo><mi>β</mi><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msup><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><msup><msub><mi>Z</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msup><msup><msub><mi>Z</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msup><msup><msub><mi>Z</mi><mrow data-mjx-texclass="ORD"><mi>S</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msup></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><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mi>exp</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>−</mo><mi>N</mi><mi>β</mi><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mi>exp</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>−</mo><mi>N</mi><mi>β</mi><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>s</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mi>exp</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>−</mo><mi>N</mi><mi>β</mi><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>s</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
Translations to Computer Algebra Systems
Translation to Maple
In Maple:
Translation to Mathematica
In Mathematica:
Similar pages
Calculated based on the variables occurring on the entire Spezifische Wärme zweiatomiger idealer Gase page
Identifiers
MathML observations
0results
0results
no statistics present please run the maintenance script ExtractFeatures.php
0 results
0 results