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Display information for equation id:math.2158.37 on revision:2158
* Page found: Wellenausbreitung in Materie (eq math.2158.37)
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Hash: 899529c4618662c6c2220ae0098b280c
TeX (original user input):
\begin{align}
& \varepsilon \left( \omega \right)=1+\frac{1}{\sqrt{2\pi }}\int_{0}^{\infty }{{}}dt\chi \left( t \right){{e}^{i\omega t}} \\
& \Rightarrow \varepsilon *(\omega )=\varepsilon (-\omega ) \\
& \varepsilon \acute{\ }(\omega )=\varepsilon \acute{\ }(-\omega ) \\
& \varepsilon \acute{\ }\acute{\ }(\omega )=-\varepsilon \acute{\ }\acute{\ }(-\omega ) \\
\end{align}
TeX (checked):
{\begin{aligned}&\varepsilon \left(\omega \right)=1+{\frac {1}{\sqrt {2\pi }}}\int _{0}^{\infty }{}dt\chi \left(t\right){{e}^{i\omega t}}\\&\Rightarrow \varepsilon *(\omega )=\varepsilon (-\omega )\\&\varepsilon {\acute {\ }}(\omega )=\varepsilon {\acute {\ }}(-\omega )\\&\varepsilon {\acute {\ }}{\acute {\ }}(\omega )=-\varepsilon {\acute {\ }}{\acute {\ }}(-\omega )\\\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"><mi>ε</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ω</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mn>1</mn><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"><msqrt><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>π</mi></mrow></msqrt></mrow></mrow></mfrac></mrow><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></msubsup><mi>d</mi><mi>t</mi><mi>χ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>ω</mi><mi>t</mi></mrow></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><mi>ε</mi><mo stretchy="false">∗</mo><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>ε</mi><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mi>ω</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>ε</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>ε</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mi>ω</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>ε</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mi>ε</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mi>ω</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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