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Display information for equation id:math.2133.12 on revision:2133

* Page found: Multipolstrahlung (eq math.2133.12)

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Hash: fba45875872780e7f683120f3696ae81

TeX (original user input): 

\bar{j}\left( \bar{r}\acute{\ },t-\frac{\left| \bar{r}-\bar{r}\acute{\ } \right|}{c} \right)\approx \bar{j}\left( \bar{r}\acute{\ },t-\frac{r}{c} \right)+\frac{\bar{r}\cdot \bar{r}\acute{\ }}{cr}\frac{\partial \bar{j}\left( \bar{r}\acute{\ },t-\frac{r}{c} \right)}{\partial \left( t-\frac{r}{c} \right)}=\bar{j}\left( \bar{r}\acute{\ },\tau  \right)+\frac{\bar{r}\cdot \bar{r}\acute{\ }}{cr}\frac{\partial \ \bar{j}\left( \bar{r}\acute{\ },\tau  \right)}{\partial \tau }

TeX (checked): 

{\bar {j}}\left({\bar {r}}{\acute {\ }},t-{\frac {\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}{c}}\right)\approx {\bar {j}}\left({\bar {r}}{\acute {\ }},t-{\frac {r}{c}}\right)+{\frac {{\bar {r}}\cdot {\bar {r}}{\acute {\ }}}{cr}}{\frac {\partial {\bar {j}}\left({\bar {r}}{\acute {\ }},t-{\frac {r}{c}}\right)}{\partial \left(t-{\frac {r}{c}}\right)}}={\bar {j}}\left({\bar {r}}{\acute {\ }},\tau \right)+{\frac {{\bar {r}}\cdot {\bar {r}}{\acute {\ }}}{cr}}{\frac {\partial \ {\bar {j}}\left({\bar {r}}{\acute {\ }},\tau \right)}{\partial \tau }}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (34.259 KB / 3.972 KB) :

j ¯ ⁢ ( r ¯ ⁢ ´ , t - | r ¯ - r ¯ ⁢ ´ | c ) ≈ j ¯ ⁢ ( r ¯ ⁢ ´ , t - r c ) + r ¯ ⋅ r ¯ ⁢ ´ c ⁢ r ⁢ ∂ ⁡ j ¯ ⁢ ( r ¯ ⁢ ´ , t - r c ) ∂ ⁡ ( t - r c ) = j ¯ ⁢ ( r ¯ ⁢ ´ , τ ) + r ¯ ⋅ r ¯ ⁢ ´ c ⁢ r ⁢ ∂ ⁡ j ¯ ⁢ ( r ¯ ⁢ ´ , τ ) ∂ ⁡ τ ¯ 𝑗 ¯ 𝑟 ´ absent 𝑡 ¯ 𝑟 ¯ 𝑟 ´ absent 𝑐 ¯ 𝑗 ¯ 𝑟 ´ absent 𝑡 𝑟 𝑐 ⋅ ¯ 𝑟 ¯ 𝑟 ´ absent 𝑐 𝑟 ¯ 𝑗 ¯ 𝑟 ´ absent 𝑡 𝑟 𝑐 𝑡 𝑟 𝑐 ¯ 𝑗 ¯ 𝑟 ´ absent 𝜏 ⋅ ¯ 𝑟 ¯ 𝑟 ´ absent 𝑐 𝑟 ¯ 𝑗 ¯ 𝑟 ´ absent 𝜏 𝜏 {\displaystyle{\displaystyle\bar{j}\left(\bar{r}\acute{\ },t-\frac{\left|\bar{% r}-\bar{r}\acute{\ }\right|}{c}\right)\approx\bar{j}\left(\bar{r}\acute{\ },t-% \frac{r}{c}\right)+\frac{\bar{r}\cdot\bar{r}\acute{\ }}{cr}\frac{\partial\bar{% j}\left(\bar{r}\acute{\ },t-\frac{r}{c}\right)}{\partial\left(t-\frac{r}{c}% \right)}=\bar{j}\left(\bar{r}\acute{\ },\tau\right)+\frac{\bar{r}\cdot\bar{r}% \acute{\ }}{cr}\frac{\partial\ \bar{j}\left(\bar{r}\acute{\ },\tau\right)}{% \partial\tau}}}

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MathML (experimentell; keine Bilder) rendering

MathML (5.595 KB / 428 B) :

j¯(r¯´,t−|r¯−r¯´|c)≈j¯(r¯´,t−rc)+r¯⋅r¯´cr∂j¯(r¯´,t−rc)∂(t−rc)=j¯(r¯´,τ)+r¯⋅r¯´cr∂j¯(r¯´,τ)∂τ

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Calculated based on the variables occurring on the entire Multipolstrahlung page

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