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Display information for equation id:math.2158.48 on revision:2158
* Page found: Wellenausbreitung in Materie (eq math.2158.48)
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Hash: 808eed9db740feeef0f61961b70ab1a4
TeX (original user input):
\begin{align}
& {{v}_{g}}:=\frac{d\omega }{dk\acute{\ }}=\frac{1}{\frac{dk\acute{\ }}{d\omega }}=\frac{c}{\frac{d\left( \omega n \right)}{d\omega }} \\
& {{v}_{g}}=\frac{c}{n+\omega \frac{dn}{d\omega }}\ne \frac{c}{n\left( \omega \right)}={{v}_{ph.}} \\
\end{align}
TeX (checked):
{\begin{aligned}&{{v}_{g}}:={\frac {d\omega }{dk{\acute {\ }}}}={\frac {1}{\frac {dk{\acute {\ }}}{d\omega }}}={\frac {c}{\frac {d\left(\omega n\right)}{d\omega }}}\\&{{v}_{g}}={\frac {c}{n+\omega {\frac {dn}{d\omega }}}}\neq {\frac {c}{n\left(\omega \right)}}={{v}_{ph.}}\\\end{aligned}}
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MathML (2.889 KB / 459 B) :
<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>v</mi><mrow data-mjx-texclass="ORD"><mi>g</mi></mrow></msub><mo stretchy="false">:=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>ω</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>k</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow></mfrac></mrow><mo stretchy="false">=</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"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>k</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>ω</mi></mrow></mrow></mfrac></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>c</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ω</mi><mi>n</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>ω</mi></mrow></mrow></mfrac></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mi>v</mi><mrow data-mjx-texclass="ORD"><mi>g</mi></mrow></msub><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>c</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">+</mo><mi>ω</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>n</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>ω</mi></mrow></mrow></mfrac></mrow></mrow></mrow></mfrac></mrow><mo stretchy="false">≠</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>c</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ω</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><msub><mi>v</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>p</mi><mi>h</mi><mo stretchy="false">.</mo></mrow></mrow></msub></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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