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Display information for equation id:math.971.28 on revision:971
* Page found: Übersicht:Thermodynamik (eq math.971.28)
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Hash: ca77ce8138633fc28542de9b479296c3
TeX (original user input):
I\left( P \right)=\sum\limits_{i}{{{P}_{i}}\ln {{P}_{i}}}=\sum\limits_{i}{{{P}_{i}}\ln \exp \left( \psi -{{\lambda }_{\nu }}M_{i}^{\nu } \right)}=\psi \underbrace{\sum\limits_{i}{{{P}_{i}}}}_{1}-{{\lambda }_{\nu }}\sum\limits_{i}{{{P}_{i}}M_{i}^{\nu }}=\psi -{{\lambda }_{\nu }}\left\langle {{M}^{\nu }} \right\rangle
TeX (checked):
I\left(P\right)=\sum \limits _{i}{{{P}_{i}}\ln {{P}_{i}}}=\sum \limits _{i}{{{P}_{i}}\ln \exp \left(\psi -{{\lambda }_{\nu }}M_{i}^{\nu }\right)}=\psi \underbrace {\sum \limits _{i}{{P}_{i}}} _{1}-{{\lambda }_{\nu }}\sum \limits _{i}{{{P}_{i}}M_{i}^{\nu }}=\psi -{{\lambda }_{\nu }}\left\langle {{M}^{\nu }}\right\rangle
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MathML (2.362 KB / 398 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>I</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>P</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><munder><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></munder><mrow data-mjx-texclass="ORD"><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mi>ln</mi><mo>⁡</mo><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow><mo>=</mo><munder><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></munder><mrow data-mjx-texclass="ORD"><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mi>ln</mi><mo>⁡</mo><mi>exp</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ψ</mi><mo>−</mo><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><msubsup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msubsup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mo>=</mo><mi>ψ</mi><munder><mrow data-mjx-texclass="OP"><munder><mrow data-mjx-texclass="ORD"><munder><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></munder><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow><mo>⏟</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></munder><mo>−</mo><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><munder><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></munder><mrow data-mjx-texclass="ORD"><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><msubsup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msubsup></mrow><mo>=</mo><mi>ψ</mi><mo>−</mo><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mstyle></mrow></math>
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