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Display information for equation id:math.1444.263 on revision:1444
* Page found: Materie in elektrischen und magnetischen Feldern (eq math.1444.263)
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Hash: 6066340b8e1c7ac73012edd400b828be
TeX (original user input):
\begin{align}
& \hat{\chi }\left( \omega \right)=\frac{1}{2\pi i}\begin{matrix}
\lim \\
\sigma ->0+ \\
\end{matrix}\int_{-\infty }^{\infty }{{}}d\omega \acute{\ }\frac{1}{\omega \acute{\ }-\omega -i\sigma }\hat{\chi }\left( \omega \acute{\ } \right) \\
& =\frac{1}{2\pi i}P\int_{-\infty }^{\infty }{{}}d\omega \acute{\ }\frac{1}{\omega \acute{\ }-\omega }\hat{\chi }\left( \omega \acute{\ } \right)+\frac{1}{2}\hat{\chi }\left( \omega \right) \\
& \Rightarrow \hat{\chi }\left( \omega \right)=\frac{1}{\pi i}P\int_{-\infty }^{\infty }{{}}d\omega \acute{\ }\frac{1}{\omega \acute{\ }-\omega }\hat{\chi }\left( \omega \acute{\ } \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&{\hat {\chi }}\left(\omega \right)={\frac {1}{2\pi i}}{\begin{matrix}\lim \\\sigma ->0+\\\end{matrix}}\int _{-\infty }^{\infty }{}d\omega {\acute {\ }}{\frac {1}{\omega {\acute {\ }}-\omega -i\sigma }}{\hat {\chi }}\left(\omega {\acute {\ }}\right)\\&={\frac {1}{2\pi i}}P\int _{-\infty }^{\infty }{}d\omega {\acute {\ }}{\frac {1}{\omega {\acute {\ }}-\omega }}{\hat {\chi }}\left(\omega {\acute {\ }}\right)+{\frac {1}{2}}{\hat {\chi }}\left(\omega \right)\\&\Rightarrow {\hat {\chi }}\left(\omega \right)={\frac {1}{\pi i}}P\int _{-\infty }^{\infty }{}d\omega {\acute {\ }}{\frac {1}{\omega {\acute {\ }}-\omega }}{\hat {\chi }}\left(\omega {\acute {\ }}\right)\\\end{aligned}}
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