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Display information for equation id:math.2133.17 on revision:2133

* Page found: Multipolstrahlung (eq math.2133.17)

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TeX (original user input): 

\begin{align}
& \int_{{}}^{{}}{{}}{{d}^{3}}r\acute{\ }{{\nabla }_{r\acute{\ }}}\left( {{x}_{k}}\acute{\ }\bar{j}\left( \bar{r}\acute{\ },\tau  \right) \right)=0=\int_{{}}^{{}}{{}}{{d}^{3}}r\acute{\ }\left( {{j}_{k}}-{{x}_{k}}\acute{\ }\dot{\rho }\left( \bar{r}\acute{\ },\tau  \right) \right) \\
& \Rightarrow \int_{{}}^{{}}{{{d}^{3}}r\acute{\ }\bar{j}\left( \bar{r}\acute{\ },\tau  \right)=\int_{{}}^{{}}{{}}{{d}^{3}}r\acute{\ }\bar{r}\acute{\ }\dot{\rho }\left( \bar{r}\acute{\ },\tau  \right)=:\dot{\bar{p}}\left( \tau  \right)} \\
\end{align}

TeX (checked): 

{\begin{aligned}&\int _{}^{}{}{{d}^{3}}r{\acute {\ }}{{\nabla }_{r{\acute {\ }}}}\left({{x}_{k}}{\acute {\ }}{\bar {j}}\left({\bar {r}}{\acute {\ }},\tau \right)\right)=0=\int _{}^{}{}{{d}^{3}}r{\acute {\ }}\left({{j}_{k}}-{{x}_{k}}{\acute {\ }}{\dot {\rho }}\left({\bar {r}}{\acute {\ }},\tau \right)\right)\\&\Rightarrow \int _{}^{}{{{d}^{3}}r{\acute {\ }}{\bar {j}}\left({\bar {r}}{\acute {\ }},\tau \right)=\int _{}^{}{}{{d}^{3}}r{\acute {\ }}{\bar {r}}{\acute {\ }}{\dot {\rho }}\left({\bar {r}}{\acute {\ }},\tau \right)=:{\dot {\bar {p}}}\left(\tau \right)}\\\end{aligned}}

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MathML (36.844 KB / 4.097 KB) :

∫ d 3 ⁢ r ⁢ ´ ⁢ ∇ r ⁢ ´ ⁡ ( x k ⁢ ´ ⁢ j ¯ ⁢ ( r ¯ ⁢ ´ , τ ) ) = 0 = ∫ d 3 ⁢ r ⁢ ´ ⁢ ( j k - x k ⁢ ´ ⁢ ρ ˙ ⁢ ( r ¯ ⁢ ´ , τ ) ) ⇒ ∫ d 3 r ´ j ¯ ( r ¯ ´ , τ ) = ∫ d 3 r ´ r ¯ ´ ρ ˙ ( r ¯ ´ , τ ) = : p ¯ ˙ ( τ ) missing-subexpression superscript 𝑑 3 𝑟 ´ absent subscript ∇ 𝑟 ´ absent subscript 𝑥 𝑘 ´ absent ¯ 𝑗 ¯ 𝑟 ´ absent 𝜏 0 superscript 𝑑 3 𝑟 ´ absent subscript 𝑗 𝑘 subscript 𝑥 𝑘 ´ absent ˙ 𝜌 ¯ 𝑟 ´ absent 𝜏 missing-subexpression fragments ⇒ superscript 𝑑 3 r ´ absent ¯ 𝑗 fragments ( ¯ 𝑟 ´ absent , τ ) superscript 𝑑 3 r ´ absent ¯ 𝑟 ´ absent ˙ 𝜌 fragments ( ¯ 𝑟 ´ absent , τ ) : ˙ ¯ 𝑝 fragments ( τ ) {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\int{{}}{{d}^{3}}r% \acute{\ }{{\nabla}_{r\acute{\ }}}\left({{x}_{k}}\acute{\ }\bar{j}\left(\bar{r% }\acute{\ },\tau\right)\right)=0=\int{{}}{{d}^{3}}r\acute{\ }\left({{j}_{k}}-{% {x}_{k}}\acute{\ }\dot{\rho}\left(\bar{r}\acute{\ },\tau\right)\right)\\ &\displaystyle\Rightarrow\int{{{d}^{3}}r\acute{\ }\bar{j}\left(\bar{r}\acute{% \ },\tau\right)=\int{{}}{{d}^{3}}r\acute{\ }\bar{r}\acute{\ }\dot{\rho}\left(% \bar{r}\acute{\ },\tau\right)=:\dot{\bar{p}}\left(\tau\right)}\\ \end{aligned}}}

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MathML (5.812 KB / 577 B) :

∫d3r´∇r´(xk´j¯(r¯´,τ))=0=∫d3r´(jk−xk´ρ˙(r¯´,τ))⇒∫d3r´j¯(r¯´,τ)=∫d3r´r¯´ρ˙(r¯´,τ)=:p¯˙(τ)

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