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Display information for equation id:math.1439.251 on revision:1439
* Page found: Elektromagnetische Wellen (eq math.1439.251)
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Hash: 49fe16503e1e1a333365ea34dc6e8687
TeX (original user input):
\begin{align}
& R=R\acute{\ }\acute{\ } \\
& d\bar{f}\cdot \frac{\bar{r}-\bar{r}\acute{\ }}{\left| \bar{r}-\bar{r}\acute{\ } \right|}=-d\bar{f}\cdot \frac{\bar{r}-\bar{r}\acute{\ }\acute{\ }}{\left| \bar{r}-\bar{r}\acute{\ }\acute{\ } \right|}=+df\cos \vartheta \\
& \Rightarrow d\bar{f}\cdot {{\nabla }_{r}}\tilde{G}=df\frac{1}{2\pi }\frac{{{e}^{ikR}}}{R}\left( ik-\frac{1}{R} \right)\cos \vartheta \\
\end{align}
TeX (checked):
{\begin{aligned}&R=R{\acute {\ }}{\acute {\ }}\\&d{\bar {f}}\cdot {\frac {{\bar {r}}-{\bar {r}}{\acute {\ }}}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}=-d{\bar {f}}\cdot {\frac {{\bar {r}}-{\bar {r}}{\acute {\ }}{\acute {\ }}}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}{\acute {\ }}\right|}}=+df\cos \vartheta \\&\Rightarrow d{\bar {f}}\cdot {{\nabla }_{r}}{\tilde {G}}=df{\frac {1}{2\pi }}{\frac {{e}^{ikR}}{R}}\left(ik-{\frac {1}{R}}\right)\cos \vartheta \\\end{aligned}}
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MathML (3.492 KB / 553 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>R</mi><mo stretchy="false">=</mo><mi>R</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>d</mi><mover><mi>f</mi><mo>¯</mo></mover><mo stretchy="false">⋅</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mi>d</mi><mover><mi>f</mi><mo>¯</mo></mover><mo stretchy="false">⋅</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mo stretchy="false">+</mo><mi>d</mi><mi>f</mi><mi>cos</mi><mo>⁡</mo><mi>ϑ</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><mi>d</mi><mover><mi>f</mi><mo>¯</mo></mover><mo stretchy="false">⋅</mo><msub><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mover><mi>G</mi><mo>~</mo></mover><mo stretchy="false">=</mo><mi>d</mi><mi>f</mi><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"><mn>2</mn><mi>π</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>k</mi><mi>R</mi></mrow></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>i</mi><mi>k</mi><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>R</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>cos</mi><mo>⁡</mo><mi>ϑ</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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