Jump to navigation
Jump to search
General
Display information for equation id:math.2158.70 on revision:2158
* Page found: Wellenausbreitung in Materie (eq math.2158.70)
(force rerendering)Occurrences on the following pages:
Hash: 912c7331fd3afaa518e5dccaacbcda99
TeX (original user input):
\begin{align}
& \operatorname{Re}\hat{\chi }\left( \omega \right)=\varepsilon \acute{\ }\left( \omega \right)-1=\frac{1}{\pi }P\int_{-\infty }^{\infty }{{}}d\omega \acute{\ }\frac{1}{\omega \acute{\ }-\omega }\varepsilon \acute{\ }\acute{\ }\left( \omega \acute{\ } \right) \\
& \operatorname{Im}\hat{\chi }\left( \omega \right)=\varepsilon \acute{\ }\acute{\ }\left( \omega \right)=-\frac{1}{\pi }P\int_{-\infty }^{\infty }{{}}d\omega \acute{\ }\frac{1}{\omega \acute{\ }-\omega }\left( \varepsilon \acute{\ }\left( \omega \acute{\ } \right)-1 \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&\operatorname {Re} {\hat {\chi }}\left(\omega \right)=\varepsilon {\acute {\ }}\left(\omega \right)-1={\frac {1}{\pi }}P\int _{-\infty }^{\infty }{}d\omega {\acute {\ }}{\frac {1}{\omega {\acute {\ }}-\omega }}\varepsilon {\acute {\ }}{\acute {\ }}\left(\omega {\acute {\ }}\right)\\&\operatorname {Im} {\hat {\chi }}\left(\omega \right)=\varepsilon {\acute {\ }}{\acute {\ }}\left(\omega \right)=-{\frac {1}{\pi }}P\int _{-\infty }^{\infty }{}d\omega {\acute {\ }}{\frac {1}{\omega {\acute {\ }}-\omega }}\left(\varepsilon {\acute {\ }}\left(\omega {\acute {\ }}\right)-1\right)\\\end{aligned}}
LaTeXML (experimental; uses MathML) rendering
MathML (0 B / 8 B) :
SVG image empty. Force Re-Rendering
SVG (0 B / 8 B) :
MathML (experimental; no images) rendering
MathML (3.951 KB / 513 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"><mo data-mjx-texclass="OP" mathvariant="normal">Re</mo><mo>⁡</mo><mover><mi>χ</mi><mo stretchy="false">̂</mo></mover><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><mi>ε</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><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"><mi>π</mi></mrow></mfrac></mrow><mi>P</mi><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mi mathvariant="normal">∞</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></msubsup><mi>d</mi><mi>ω</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><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"><mi>ω</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">−</mo><mi>ω</mi></mrow></mrow></mfrac></mrow><mi>ε</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ω</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo data-mjx-texclass="OP" mathvariant="normal">Im</mo><mo>⁡</mo><mover><mi>χ</mi><mo stretchy="false">̂</mo></mover><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><mi>ε</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><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><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>π</mi></mrow></mfrac></mrow><mi>P</mi><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mi mathvariant="normal">∞</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></msubsup><mi>d</mi><mi>ω</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><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"><mi>ω</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">−</mo><mi>ω</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ε</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ω</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">−</mo><mn>1</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
Translations to Computer Algebra Systems
Translation to Maple
In Maple:
Translation to Mathematica
In Mathematica:
Similar pages
Calculated based on the variables occurring on the entire Wellenausbreitung in Materie page
Identifiers
MathML observations
0results
0results
no statistics present please run the maintenance script ExtractFeatures.php
0 results
0 results