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Display information for equation id:math.2577.12 on revision:2577
* Page found: Spezifische Wärme von Festkörpern (eq math.2577.12)
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Hash: a25f0342a491e4d1ac604b051d48192b
TeX (original user input):
U=\frac{9N}{{{\omega }_{D}}^{3}}\int_{0}^{{{\omega }_{D}}}{{}}d\omega {{\omega }^{2}}\left( \frac{1}{{{e}^{\beta \hbar \omega }}-1}+\frac{1}{2} \right)\hbar \omega
TeX (checked):
U={\frac {9N}{{{\omega }_{D}}^{3}}}\int _{0}^{{\omega }_{D}}{}d\omega {{\omega }^{2}}\left({\frac {1}{{{e}^{\beta \hbar \omega }}-1}}+{\frac {1}{2}}\right)\hbar \omega
LaTeXML (experimentell; verwendet MathML) rendering
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MathML (1.542 KB / 387 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="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>9</mn><mi>N</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><msup><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mi>D</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mfrac></mrow><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mi>D</mi></mrow></msub></mrow></munderover></mstyle><mi>d</mi><mi>ω</mi><msup><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</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"><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>β</mi><mi data-mjx-alternate="1">ℏ</mi><mi>ω</mi></mrow></mrow></msup><mo>−</mo><mn>1</mn></mrow></mrow></mfrac></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi data-mjx-alternate="1">ℏ</mi><mi>ω</mi></mstyle></mrow></math>
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