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Display information for equation id:math.949.0 on revision:949
* Page found: Kanonisches Enseble (eq math.949.0)
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Hash: 32a40bf4c3d6a15e150c008c6bb10b60
TeX (original user input):
U=\left\langle E \right\rangle =\frac{1}{Z\left( \beta ,N \right)}\sum\limits_{\alpha }{{{E}_{\alpha }}\exp \left( -\beta {{E}_{\alpha }} \right)}=-{{\partial }_{\beta }}\ln \left( Z\left( \beta ,N \right) \right)
TeX (checked):
U=\left\langle E\right\rangle ={\frac {1}{Z\left(\beta ,N\right)}}\sum \limits _{\alpha }{{{E}_{\alpha }}\exp \left(-\beta {{E}_{\alpha }}\right)}=-{{\partial }_{\beta }}\ln \left(Z\left(\beta ,N\right)\right)
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MathML (1.515 KB / 365 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>U</mi><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>E</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><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>Z</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>β</mi><mo>,</mo><mi>N</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow></mfrac></mrow><munder><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></munder><mrow data-mjx-texclass="ORD"><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msub><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>α</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mo>=</mo><mo>−</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>β</mi></mrow></msub><mi>ln</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>Z</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>β</mi><mo>,</mo><mi>N</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mstyle></mrow></math>
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