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Display information for equation id:math.2567.39 on revision:2567
* Page found: Das Photonengas im Strahlungshohlraum (eq math.2567.39)
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Hash: b6038af9c6e10370f3edbb7e78bc01b6
TeX (original user input):
\begin{align}
& {{B}_{12}}u\left( \nu ,T \right)\left\langle {{N}_{1}} \right\rangle ={{B}_{21}}u\left( \nu ,T \right)\left\langle {{N}_{2}} \right\rangle +{{A}_{21}}\left\langle {{N}_{2}} \right\rangle \\
& \Rightarrow u\left( \nu ,T \right)=\frac{{{A}_{21}}}{{{B}_{12}}\frac{\left\langle {{N}_{1}} \right\rangle }{\left\langle {{N}_{2}} \right\rangle }-{{B}_{21}}}=\frac{{{A}_{21}}}{{{B}_{12}}\frac{{{g}_{1}}}{{{g}_{2}}}{{e}^{\beta h\nu }}-{{B}_{21}}} \\
\end{align}
TeX (checked):
{\begin{aligned}&{{B}_{12}}u\left(\nu ,T\right)\left\langle {{N}_{1}}\right\rangle ={{B}_{21}}u\left(\nu ,T\right)\left\langle {{N}_{2}}\right\rangle +{{A}_{21}}\left\langle {{N}_{2}}\right\rangle \\&\Rightarrow u\left(\nu ,T\right)={\frac {{A}_{21}}{{{B}_{12}}{\frac {\left\langle {{N}_{1}}\right\rangle }{\left\langle {{N}_{2}}\right\rangle }}-{{B}_{21}}}}={\frac {{A}_{21}}{{{B}_{12}}{\frac {{g}_{1}}{{g}_{2}}}{{e}^{\beta h\nu }}-{{B}_{21}}}}\\\end{aligned}}
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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"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mi>B</mi><mrow data-mjx-texclass="ORD"><mn>12</mn></mrow></msub><mi>u</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ν</mi><mo>,</mo><mi>T</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">=</mo><msub><mi>B</mi><mrow data-mjx-texclass="ORD"><mn>21</mn></mrow></msub><mi>u</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ν</mi><mo>,</mo><mi>T</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">+</mo><msub><mi>A</mi><mrow data-mjx-texclass="ORD"><mn>21</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><mi>u</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ν</mi><mo>,</mo><mi>T</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>A</mi><mrow data-mjx-texclass="ORD"><mn>21</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>B</mi><mrow data-mjx-texclass="ORD"><mn>12</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mrow></mfrac></mrow><mo stretchy="false">−</mo><msub><mi>B</mi><mrow data-mjx-texclass="ORD"><mn>21</mn></mrow></msub></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>A</mi><mrow data-mjx-texclass="ORD"><mn>21</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>B</mi><mrow data-mjx-texclass="ORD"><mn>12</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>g</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>g</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mfrac></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>β</mi><mi>h</mi><mi>ν</mi></mrow></mrow></msup><mo stretchy="false">−</mo><msub><mi>B</mi><mrow data-mjx-texclass="ORD"><mn>21</mn></mrow></msub></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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