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Display information for equation id:math.1438.250 on revision:1438
* Page found: Elektromagnetische Wellen (eq math.1438.250)
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\begin{align}
& {{\nabla }_{r}}\tilde{G}\left( \bar{r}-\bar{r}\acute{\ } \right)=\frac{1}{4\pi }\left( {{\nabla }_{r}}\frac{{{e}^{ik\left| \bar{r}-\bar{r}\acute{\ } \right|}}}{\left| \bar{r}-\bar{r}\acute{\ } \right|}-{{\nabla }_{r}}\frac{{{e}^{ik\left| \bar{r}-\bar{r}\acute{\ }\acute{\ } \right|}}}{\left| \bar{r}-\bar{r}\acute{\ }\acute{\ } \right|} \right):=\frac{1}{4\pi }\left( {{\nabla }_{r}}\frac{{{e}^{ikR}}}{R}-{{\nabla }_{r}}\frac{{{e}^{ikR\acute{\ }\acute{\ }}}}{R\acute{\ }\acute{\ }} \right) \\
& =\frac{1}{4\pi }\left( \frac{{{e}^{ikR}}}{R}\left( ik-\frac{1}{R} \right)\frac{\bar{r}-\bar{r}\acute{\ }}{\left| \bar{r}-\bar{r}\acute{\ } \right|}-\frac{{{e}^{ikR\acute{\ }\acute{\ }}}}{R\acute{\ }\acute{\ }}\left( ik-\frac{1}{R\acute{\ }\acute{\ }} \right)\frac{\bar{r}-\bar{r}\acute{\ }\acute{\ }}{\left| \bar{r}-\bar{r}\acute{\ }\acute{\ } \right|} \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\nabla }_{r}}{\tilde {G}}\left({\bar {r}}-{\bar {r}}{\acute {\ }}\right)={\frac {1}{4\pi }}\left({{\nabla }_{r}}{\frac {{e}^{ik\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}-{{\nabla }_{r}}{\frac {{e}^{ik\left|{\bar {r}}-{\bar {r}}{\acute {\ }}{\acute {\ }}\right|}}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}{\acute {\ }}\right|}}\right):={\frac {1}{4\pi }}\left({{\nabla }_{r}}{\frac {{e}^{ikR}}{R}}-{{\nabla }_{r}}{\frac {{e}^{ikR{\acute {\ }}{\acute {\ }}}}{R{\acute {\ }}{\acute {\ }}}}\right)\\&={\frac {1}{4\pi }}\left({\frac {{e}^{ikR}}{R}}\left(ik-{\frac {1}{R}}\right){\frac {{\bar {r}}-{\bar {r}}{\acute {\ }}}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}-{\frac {{e}^{ikR{\acute {\ }}{\acute {\ }}}}{R{\acute {\ }}{\acute {\ }}}}\left(ik-{\frac {1}{R{\acute {\ }}{\acute {\ }}}}\right){\frac {{\bar {r}}-{\bar {r}}{\acute {\ }}{\acute {\ }}}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}{\acute {\ }}\right|}}\right)\\\end{aligned}}
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