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* Page found: Materie in elektrischen und magnetischen Feldern (eq math.1444.258)

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\int_{-\infty }^{\infty }{{}}d\omega \acute{\ }\frac{1}{\omega \acute{\ }-\omega }\hat{\chi }\left( \omega \acute{\ } \right)=\begin{matrix}
\lim   \\
\varepsilon ->{{0}^{+}}  \\
\end{matrix}\left[ \int_{-\infty }^{\omega -\varepsilon }{+\int_{\omega +\varepsilon }^{\infty }{{}}} \right]d\omega \acute{\ }\frac{1}{\omega \acute{\ }-\omega }\hat{\chi }\left( \omega \acute{\ } \right)+\int\limits_{Kreisbogen}{{}}d\omega \acute{\ }\frac{1}{\omega \acute{\ }-\omega }\hat{\chi }\left( \omega \acute{\ } \right)

TeX (checked): 

\int _{-\infty }^{\infty }{}d\omega {\acute {\ }}{\frac {1}{\omega {\acute {\ }}-\omega }}{\hat {\chi }}\left(\omega {\acute {\ }}\right)={\begin{matrix}\lim \\\varepsilon ->{{0}^{+}}\\\end{matrix}}\left[\int _{-\infty }^{\omega -\varepsilon }{+\int _{\omega +\varepsilon }^{\infty }{}}\right]d\omega {\acute {\ }}{\frac {1}{\omega {\acute {\ }}-\omega }}{\hat {\chi }}\left(\omega {\acute {\ }}\right)+\int \limits _{Kreisbogen}{}d\omega {\acute {\ }}{\frac {1}{\omega {\acute {\ }}-\omega }}{\hat {\chi }}\left(\omega {\acute {\ }}\right)

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∫ - ∞ ∞ 𝑑 ω ⁢ ´ ⁢ 1 ω ⁢ ´ - ω ⁢ χ ^ ⁢ ( ω ⁢ ´ ) = lim ε - > 0 + ⁢ [ ∫ - ∞ ω - ε + ∫ ω + ε ∞ ] ⁢ d ⁢ ω ⁢ ´ ⁢ 1 ω ⁢ ´ - ω ⁢ χ ^ ⁢ ( ω ⁢ ´ ) + ∫ K ⁢ r ⁢ e ⁢ i ⁢ s ⁢ b ⁢ o ⁢ g ⁢ e ⁢ n 𝑑 ω ⁢ ´ ⁢ 1 ω ⁢ ´ - ω ⁢ χ ^ ⁢ ( ω ⁢ ´ ) superscript subscript differential-d 𝜔 ´ absent 1 𝜔 ´ absent 𝜔 ^ 𝜒 𝜔 ´ absent limit-from 𝜀 superscript 0 delimited-[] superscript subscript 𝜔 𝜀 superscript subscript 𝜔 𝜀 𝑑 𝜔 ´ absent 1 𝜔 ´ absent 𝜔 ^ 𝜒 𝜔 ´ absent subscript 𝐾 𝑟 𝑒 𝑖 𝑠 𝑏 𝑜 𝑔 𝑒 𝑛 differential-d 𝜔 ´ absent 1 𝜔 ´ absent 𝜔 ^ 𝜒 𝜔 ´ absent {\displaystyle{\displaystyle\int_{-\infty}^{\infty}{{}}d\omega\acute{\ }\frac{% 1}{\omega\acute{\ }-\omega}\hat{\chi}\left(\omega\acute{\ }\right)=\begin{% matrix}\lim\\ \varepsilon->{{0}^{+}}\\ \end{matrix}\left[\int_{-\infty}^{\omega-\varepsilon}{+\int_{\omega+% \varepsilon}^{\infty}{{}}}\right]d\omega\acute{\ }\frac{1}{\omega\acute{\ }-% \omega}\hat{\chi}\left(\omega\acute{\ }\right)+\int\limits_{Kreisbogen}{{}}d% \omega\acute{\ }\frac{1}{\omega\acute{\ }-\omega}\hat{\chi}\left(\omega\acute{% \ }\right)}}

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∫−∞∞dω´1ω´−ωχ^(ω´)=limε−>0+[∫−∞ω−ε+∫ω+ε∞]dω´1ω´−ωχ^(ω´)+∫Kreisbogendω´1ω´−ωχ^(ω´)

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