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Display information for equation id:math.2159.59 on revision:2159
* Page found: Wellenausbreitung in Materie (eq math.2159.59)
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Hash: da151c1c51d73ea54955fac938a4da85
TeX (original user input):
\begin{align}
& \hat{\Theta }\left( \omega \right):=\begin{matrix}
\lim \\
\sigma ->0+ \\
\end{matrix}\frac{1}{\sqrt{2\pi }}\int_{0}^{\infty }{dt{{e}^{i\omega t-\sigma t}}}=\begin{matrix}
\lim \\
\sigma ->0+ \\
\end{matrix}\frac{1}{\sqrt{2\pi }}\frac{1}{i\omega -\sigma } \\
& \\
\end{align}
TeX (checked):
{\begin{aligned}&{\hat {\Theta }}\left(\omega \right):={\begin{matrix}\lim \\\sigma ->0+\\\end{matrix}}{\frac {1}{\sqrt {2\pi }}}\int _{0}^{\infty }{dt{{e}^{i\omega t-\sigma t}}}={\begin{matrix}\lim \\\sigma ->0+\\\end{matrix}}{\frac {1}{\sqrt {2\pi }}}{\frac {1}{i\omega -\sigma }}\\&\\\end{aligned}}
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MathML (2.403 KB / 505 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"><mover><mi>Θ</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><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN"></mo><mtable><mtr><mtd><mo>lim</mo></mtd></mtr><mtr><mtd><mi>σ</mi><mo stretchy="false">−</mo><mo>></mo><mn>0</mn><mo stretchy="false">+</mo></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true" data-mjx-texclass="CLOSE"></mo></mrow><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><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>ω</mi><mi>t</mi><mo stretchy="false">−</mo><mi>σ</mi><mi>t</mi></mrow></mrow></msup></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN"></mo><mtable><mtr><mtd><mo>lim</mo></mtd></mtr><mtr><mtd><mi>σ</mi><mo stretchy="false">−</mo><mo>></mo><mn>0</mn><mo stretchy="false">+</mo></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true" data-mjx-texclass="CLOSE"></mo></mrow><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><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>i</mi><mi>ω</mi><mo stretchy="false">−</mo><mi>σ</mi></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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