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Display information for equation id:math.1438.253 on revision:1438

* Page found: Elektromagnetische Wellen (eq math.1438.253)

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Hash: 2a38428d43d503b31b6eacb819ce2e15

TeX (original user input):

\Phi \left( \bar{r}\acute{\ } \right)=-\int_{\partial V}^{{}}{d\bar{f}\Phi \left( {\bar{r}} \right){{\nabla }_{r}}\tilde{G}\left( \bar{r}-\bar{r}\acute{\ } \right)}=-\frac{i}{\lambda }\int_{F}^{{}}{df\Phi \left( {\bar{r}} \right)\frac{{{e}^{ik\left| \bar{r}-\bar{r}\acute{\ } \right|}}}{\left| \bar{r}-\bar{r}\acute{\ } \right|}}\cos \vartheta

TeX (checked):

\Phi \left({\bar {r}}{\acute {\ }}\right)=-\int _{\partial V}^{}{d{\bar {f}}\Phi \left({\bar {r}}\right){{\nabla }_{r}}{\tilde {G}}\left({\bar {r}}-{\bar {r}}{\acute {\ }}\right)}=-{\frac {i}{\lambda }}\int _{F}^{}{df\Phi \left({\bar {r}}\right){\frac {{e}^{ik\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}}\cos \vartheta

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Φ(r¯´)=Vdf¯Φ(r¯)rG~(r¯r¯´)=iλFdfΦ(r¯)eik|r¯r¯´||r¯r¯´|cosϑ
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi mathvariant="normal">&#x03A6;</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mo>&#x2212;</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>V</mi></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mi>d</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>f</mi><mo>¯</mo></mover></mrow></mrow><mi mathvariant="normal">&#x03A6;</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><msub><mi mathvariant="normal">&#x2207;</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>G</mi><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mo>=</mo><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow><mrow data-mjx-texclass="ORD"><mi>&#x03BB;</mi></mrow></mfrac></mrow><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><mi>F</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>f</mi><mi mathvariant="normal">&#x03A6;</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></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><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow></mfrac></mrow></mrow><mi>cos</mi><mo>&#x2061;</mo><mi>&#x03D1;</mi></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Elektromagnetische Wellen page

Identifiers

  • Φ
  • r¯
  • ´
  • V
  • f¯
  • Φ
  • r¯
  • r
  • G~
  • r¯
  • r¯
  • ´
  • i
  • λ
  • F
  • f
  • Φ
  • r¯
  • e
  • i
  • k
  • r¯
  • r¯
  • ´
  • r¯
  • r¯
  • ´
  • ϑ

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