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Display information for equation id:math.2174.20 on revision:2174
* Page found: Transformationsverhalten der Ströme und Felder (eq math.2174.20)
(force rerendering)Occurrences on the following pages:
Hash: d7021119cdb76060ff3b906c3263a532
TeX (original user input):
\begin{align}
& \tilde{\bar{A}}=\bar{A}+\nabla F \\
& \tilde{\phi }=\phi -\frac{\partial }{\partial t}F \\
& \Leftrightarrow \\
& c{{{\tilde{A}}}^{\alpha }}=c{{A}^{\alpha }}+{{\partial }_{\alpha }}cF=c{{A}^{\alpha }}-{{\partial }^{\alpha }}cF \\
& {{{\tilde{\Phi }}}^{0}}={{\Phi }^{0}}-{{\partial }_{0}}cF={{\Phi }^{0}}-{{\partial }^{0}}cF \\
\end{align}
TeX (checked):
{\begin{aligned}&{\tilde {\bar {A}}}={\bar {A}}+\nabla F\\&{\tilde {\phi }}=\phi -{\frac {\partial }{\partial t}}F\\&\Leftrightarrow \\&c{{\tilde {A}}^{\alpha }}=c{{A}^{\alpha }}+{{\partial }_{\alpha }}cF=c{{A}^{\alpha }}-{{\partial }^{\alpha }}cF\\&{{\tilde {\Phi }}^{0}}={{\Phi }^{0}}-{{\partial }_{0}}cF={{\Phi }^{0}}-{{\partial }^{0}}cF\\\end{aligned}}
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MathML (2.564 KB / 472 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mo>+</mo><mi mathvariant="normal">∇</mi><mi>F</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ϕ</mi><mo>~</mo></mover></mrow></mrow><mo>=</mo><mi>ϕ</mi><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mi>F</mi></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇔</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi>c</mi><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup><mo>=</mo><mi>c</mi><msup><mi>A</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup><mo>+</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msub><mi>c</mi><mi>F</mi><mo>=</mo><mi>c</mi><msup><mi>A</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup><mo>−</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup><mi>c</mi><mi>F</mi></mtd></mtr><mtr><mtd></mtd><mtd><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi mathvariant="normal">Φ</mi><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo>=</mo><msup><mi mathvariant="normal">Φ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo>−</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>c</mi><mi>F</mi><mo>=</mo><msup><mi mathvariant="normal">Φ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo>−</mo><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mi>c</mi><mi>F</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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