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Display information for equation id:math.2137.18 on revision:2137

* Page found: Wellenoptik und Beugung (eq math.2137.18)

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TeX (original user input): 

\begin{align}
& \Phi \left( \bar{r}\acute{\ } \right)=\int_{\partial V}^{{}}{d\bar{f}}\left( \tilde{G}\left( \bar{r}-\bar{r}\acute{\ } \right)\nabla \Phi \left( {\bar{r}} \right)-\Phi \left( {\bar{r}} \right)\nabla \tilde{G}\left( \bar{r}-\bar{r}\acute{\ } \right) \right) \\
& \bar{r}\acute{\ }\in V \\
\end{align}

TeX (checked): 

{\begin{aligned}&\Phi \left({\bar {r}}{\acute {\ }}\right)=\int _{\partial V}^{}{d{\bar {f}}}\left({\tilde {G}}\left({\bar {r}}-{\bar {r}}{\acute {\ }}\right)\nabla \Phi \left({\bar {r}}\right)-\Phi \left({\bar {r}}\right)\nabla {\tilde {G}}\left({\bar {r}}-{\bar {r}}{\acute {\ }}\right)\right)\\&{\bar {r}}{\acute {\ }}\in V\\\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (23.583 KB / 2.686 KB) :

Φ ⁢ ( r ¯ ⁢ ´ ) = ∫ ∂ ⁡ V 𝑑 f ¯ ⁢ ( G ~ ⁢ ( r ¯ - r ¯ ⁢ ´ ) ⁢ ∇ ⁡ Φ ⁢ ( r ¯ ) - Φ ⁢ ( r ¯ ) ⁢ ∇ ⁡ G ~ ⁢ ( r ¯ - r ¯ ⁢ ´ ) ) r ¯ ⁢ ´ ∈ V missing-subexpression Φ ¯ 𝑟 ´ absent subscript 𝑉 differential-d ¯ 𝑓 ~ 𝐺 ¯ 𝑟 ¯ 𝑟 ´ absent ∇ Φ ¯ 𝑟 Φ ¯ 𝑟 ∇ ~ 𝐺 ¯ 𝑟 ¯ 𝑟 ´ absent missing-subexpression ¯ 𝑟 ´ absent 𝑉 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\Phi\left(\bar{r}% \acute{\ }\right)=\int_{\partial V}{d\bar{f}}\left(\tilde{G}\left(\bar{r}-\bar% {r}\acute{\ }\right)\nabla\Phi\left({\bar{r}}\right)-\Phi\left({\bar{r}}\right% )\nabla\tilde{G}\left(\bar{r}-\bar{r}\acute{\ }\right)\right)\\ &\displaystyle\bar{r}\acute{\ }\in V\\ \end{aligned}}}

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MathML (3.455 KB / 483 B) :

Φ(r¯´)=∫∂Vdf¯(G~(r¯−r¯´)∇Φ(r¯)−Φ(r¯)∇G~(r¯−r¯´))r¯´∈V

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Identifiers

  • Φ
  • r¯
  • ´
  • V
  • f¯
  • G~
  • r¯
  • r¯
  • ´
  • Φ
  • r¯
  • Φ
  • r¯
  • G~
  • r¯
  • r¯
  • ´
  • r¯
  • ´
  • V

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