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Display information for equation id:math.983.1 on revision:983
* Page found: Gase (eq math.983.1)
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Hash: a354ccf7daf8c8982150795ebb7457cd
TeX (original user input):
\Xi =\sum\limits_{{{N}_{1}},...{{N}_{l}}}{\exp \left( -\beta \underbrace{\sum\limits_{j=1}^{l}{\left( {{E}_{j}}-\mu \right){{N}_{j}}}}_{\text{Besetzungszahl}} \right)=\prod\limits_{j=1}^{l}{\underbrace{\sum\limits_{{{N}_{j}}}{\exp \left( -\beta \left( {{E}_{j}}-\mu \right){{N}_{j}} \right)}}_{\text{Teilchenzahl}}}}\underbrace{=}_{\text{Fermionen}}\prod\limits_{j=1}^{l}{1+\exp \left( -\beta \left( {{E}_{j}}-\mu \right) \right)}
TeX (checked):
\Xi =\sum \limits _{{{N}_{1}},...{{N}_{l}}}{\exp \left(-\beta \underbrace {\sum \limits _{j=1}^{l}{\left({{E}_{j}}-\mu \right){{N}_{j}}}} _{\text{Besetzungszahl}}\right)=\prod \limits _{j=1}^{l}{\underbrace {\sum \limits _{{N}_{j}}{\exp \left(-\beta \left({{E}_{j}}-\mu \right){{N}_{j}}\right)}} _{\text{Teilchenzahl}}}}\underbrace {=} _{\text{Fermionen}}\prod \limits _{j=1}^{l}{1+\exp \left(-\beta \left({{E}_{j}}-\mu \right)\right)}
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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"><mi>Ξ</mi><mo stretchy="false">=</mo><munder><mo form="prefix" movablelimits="false" stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mi>...</mi><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub></mrow></mrow></munder><mrow data-mjx-texclass="ORD"><mi>exp</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo stretchy="false">−</mo><mi>β</mi><munder><mrow data-mjx-texclass="OP"><munder><mrow data-mjx-texclass="ORD"><munderover><mo form="prefix" movablelimits="false" stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>j</mi><mo stretchy="false">=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo stretchy="false">−</mo><mi>μ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></mrow></mrow><mo>⏟</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>Besetzungszahl</mtext></mrow></mrow></munder><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>j</mi><mo stretchy="false">=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></munderover><munder><mrow data-mjx-texclass="OP"><munder><mrow data-mjx-texclass="ORD"><munder><mo form="prefix" movablelimits="false" stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></mrow></munder><mrow data-mjx-texclass="ORD"><mi>exp</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo stretchy="false">−</mo><mi>β</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo stretchy="false">−</mo><mi>μ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow><mo>⏟</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>Teilchenzahl</mtext></mrow></mrow></munder></mrow><munder><mrow data-mjx-texclass="OP"><munder><mo stretchy="false" lspace="0" rspace="0">=</mo><mo>⏟</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>Fermionen</mtext></mrow></mrow></munder><munderover><mo form="prefix" movablelimits="false" stretchy="false">∏</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>j</mi><mo stretchy="false">=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><mn>1</mn><mo stretchy="false">+</mo><mi>exp</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo stretchy="false">−</mo><mi>β</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo stretchy="false">−</mo><mi>μ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mstyle></mrow></math>
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