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Display information for equation id:math.1443.232 on revision:1443
* Page found: Materie in elektrischen und magnetischen Feldern (eq math.1443.232)
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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}
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<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>ε</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ω</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mn>1</mn><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"><msqrt><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>π</mi></mrow></msqrt></mrow></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"><mi mathvariant="normal">∞</mi></mrow></munderover></mstyle><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></mtd><mtd><mo>⇒</mo><mi>ε</mi><mo>*</mo><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo>=</mo><mi>ε</mi><mo stretchy="false">(</mo><mo>−</mo><mi>ω</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi>ε</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo>=</mo><mi>ε</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mo>−</mo><mi>ω</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi>ε</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo>=</mo><mo>−</mo><mi>ε</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mo>−</mo><mi>ω</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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