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Display information for equation id:math.1439.112 on revision:1439
* Page found: Elektromagnetische Wellen (eq math.1439.112)
(force rerendering)Occurrences on the following pages:
Hash: 79f99c524150eed59266482f48b311a9
TeX (original user input):
\begin{align}
& \omega =R\cdot {{e}^{i\phi }}\quad \pi \le \phi \le 2\pi \\
& d\omega =R\cdot {{e}^{i\phi }}id\phi \\
& \left| {{e}^{-i\omega \tau }} \right|={{e}^{R\sin \phi \tau }} \\
& \sin \phi <0 \\
& \tau >0 \\
& \Rightarrow \begin{matrix}
\lim \\
R\to \infty \\
\end{matrix}{{e}^{R\sin \phi \tau }}=0 \\
\end{align}
TeX (checked):
{\begin{aligned}&\omega =R\cdot {{e}^{i\phi }}\quad \pi \leq \phi \leq 2\pi \\&d\omega =R\cdot {{e}^{i\phi }}id\phi \\&\left|{{e}^{-i\omega \tau }}\right|={{e}^{R\sin \phi \tau }}\\&\sin \phi <0\\&\tau >0\\&\Rightarrow {\begin{matrix}\lim \\R\to \infty \\\end{matrix}}{{e}^{R\sin \phi \tau }}=0\\\end{aligned}}
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MathML (2.443 KB / 516 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"><mi>ω</mi><mo stretchy="false">=</mo><mi>R</mi><mo stretchy="false">⋅</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>ϕ</mi></mrow></mrow></msup><mspace width="1em"></mspace><mi>π</mi><mo stretchy="false">≤</mo><mi>ϕ</mi><mo stretchy="false">≤</mo><mn>2</mn><mi>π</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>d</mi><mi>ω</mi><mo stretchy="false">=</mo><mi>R</mi><mo stretchy="false">⋅</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>ϕ</mi></mrow></mrow></msup><mi>i</mi><mi>d</mi><mi>ϕ</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mi>i</mi><mi>ω</mi><mi>τ</mi></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">|</mo></mrow><mo stretchy="false">=</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>R</mi><mi>sin</mi><mo>⁡</mo><mi>ϕ</mi><mi>τ</mi></mrow></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>sin</mi><mo>⁡</mo><mi>ϕ</mi><mo><</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>τ</mi><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><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>R</mi><mo stretchy="false" accent="false">→</mo><mi mathvariant="normal">∞</mi></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true" data-mjx-texclass="CLOSE"></mo></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>R</mi><mi>sin</mi><mo>⁡</mo><mi>ϕ</mi><mi>τ</mi></mrow></mrow></msup><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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