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Display information for equation id:math.2075.41 on revision:2075
* Page found: Poisson- Gleichung und Greensche Funktion (eq math.2075.41)
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Hash: a79dc50281d6fc6c8d9a71f945b8beeb
TeX (original user input):
\Phi (\bar{r})=\int_{-\infty }^{\infty }{{}}\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\rho (\bar{r}\acute{\ })}{|\bar{r}-\bar{r}\acute{\ }|}{{d}^{3}}r\acute{\ }=\int_{-\infty }^{\infty }{{}}G(\bar{r}-\bar{r}\acute{\ })\rho (\bar{r}\acute{\ }){{d}^{3}}r\acute{\ }
TeX (checked):
\Phi ({\bar {r}})=\int _{-\infty }^{\infty }{}{\frac {1}{4\pi {{\varepsilon }_{0}}}}{\frac {\rho ({\bar {r}}{\acute {\ }})}{|{\bar {r}}-{\bar {r}}{\acute {\ }}|}}{{d}^{3}}r{\acute {\ }}=\int _{-\infty }^{\infty }{}G({\bar {r}}-{\bar {r}}{\acute {\ }})\rho ({\bar {r}}{\acute {\ }}){{d}^{3}}r{\acute {\ }}
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<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>Φ</mi><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mi mathvariant="normal">∞</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></msubsup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>π</mi><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>ρ</mi><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">|</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">|</mo></mrow></mrow></mfrac></mrow><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">=</mo><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mi mathvariant="normal">∞</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></msubsup><mi>G</mi><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">)</mo><mi>ρ</mi><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">)</mo><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mstyle></mrow></math>
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