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Display information for equation id:math.2584.30 on revision:2584
* Page found: Paramagnetismus (eq math.2584.30)
(force rerendering)Occurrences on the following pages:
Hash: dc0c0815eab168519ba347935c658189
TeX (original user input):
\begin{align}
& M=\frac{N}{V}\frac{1}{\beta }\frac{\partial }{\partial B}\ln Z=\frac{N}{V}\frac{B}{\sinh \left( \beta mB \right)}\frac{1}{\beta }\frac{\partial }{\partial B}\left( \frac{\sinh \left( \beta mB \right)}{B} \right) \\
& =\frac{N}{V}m\left( \coth \left( \beta mB \right)-\frac{1}{\beta mB} \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&M={\frac {N}{V}}{\frac {1}{\beta }}{\frac {\partial }{\partial B}}\ln Z={\frac {N}{V}}{\frac {B}{\sinh \left(\beta mB\right)}}{\frac {1}{\beta }}{\frac {\partial }{\partial B}}\left({\frac {\sinh \left(\beta mB\right)}{B}}\right)\\&={\frac {N}{V}}m\left(\coth \left(\beta mB\right)-{\frac {1}{\beta mB}}\right)\\\end{aligned}}
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MathML (2.988 KB / 429 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>M</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>β</mi></mrow></mfrac></mrow><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>B</mi></mrow></mrow></mfrac></mrow><mi>ln</mi><mo>⁡</mo><mi>Z</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>B</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>sinh</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>β</mi><mi>m</mi><mi>B</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>β</mi></mrow></mfrac></mrow><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>B</mi></mrow></mrow></mfrac></mrow><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>sinh</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>β</mi><mi>m</mi><mi>B</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>B</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow></mfrac></mrow><mi>m</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>coth</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>β</mi><mi>m</mi><mi>B</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>β</mi><mi>m</mi><mi>B</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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