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Display information for equation id:math.2585.50 on revision:2585
* Page found: Paramagnetismus (eq math.2585.50)
(force rerendering)Occurrences on the following pages:
Hash: a32b5143051d130457a9418c6bfae276
TeX (original user input):
\begin{align}
& S\left( T \right)=kN\left( \ln Z-\beta \frac{\partial }{\partial \beta }\ln Z \right) \\
& S\left( T \right)=kN\left[ \ln 2+\ln \cosh \left( \frac{\beta \mu B}{2} \right)-\frac{\beta \mu B}{2}\tanh \left( \frac{\beta \mu B}{2} \right) \right] \\
\end{align}
TeX (checked):
{\begin{aligned}&S\left(T\right)=kN\left(\ln Z-\beta {\frac {\partial }{\partial \beta }}\ln Z\right)\\&S\left(T\right)=kN\left[\ln 2+\ln \cosh \left({\frac {\beta \mu B}{2}}\right)-{\frac {\beta \mu B}{2}}\tanh \left({\frac {\beta \mu B}{2}}\right)\right]\\\end{aligned}}
LaTeXML (experimental; uses MathML) rendering
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MathML (experimental; no images) rendering
MathML (2.322 KB / 418 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>S</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>T</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi>k</mi><mi>N</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ln</mi><mo>⁡</mo><mi>Z</mi><mo>−</mo><mi>β</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>β</mi></mrow></mrow></mfrac></mrow><mi>ln</mi><mo>⁡</mo><mi>Z</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>S</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>T</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi>k</mi><mi>N</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mi>ln</mi><mo>⁡</mo><mn>2</mn><mo>+</mo><mi>ln</mi><mo>⁡</mo><mi>cosh</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>β</mi><mi>μ</mi><mi>B</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>β</mi><mi>μ</mi><mi>B</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mi>tanh</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>β</mi><mi>μ</mi><mi>B</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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