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Display information for equation id:math.1109.54 on revision:1109
* Page found: ART-Skript (eq math.1109.54)
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Hash: 4d31c4427f078098e25d4ffa107cf14a
TeX (original user input):
\left( \frac{\partial {{v}^{\beta }}}{\partial {{x}^{\alpha }}} \right)'={{v}^{\beta }}_{,\alpha }'=\frac{\partial v{{'}^{\beta }}}{\partial x{{'}^{\alpha }}}=\frac{\partial }{\partial x{{'}^{\alpha }}}\left( \Lambda _{\sigma }^{\beta }{{v}^{\sigma }} \right)=\Lambda _{\sigma }^{\beta }\frac{\partial {{v}^{\sigma }}}{\partial x{{'}^{\alpha }}}=\Lambda _{\sigma }^{\beta }\frac{\partial {{v}^{\sigma }}}{\partial {{x}^{\rho }}}\frac{\partial {{x}^{\rho }}}{\partial x{{'}^{\alpha }}}=\Lambda _{\sigma }^{\beta }\bar{\Lambda }_{\alpha }^{\rho }\frac{\partial {{v}^{\sigma }}}{\partial {{x}^{\rho }}}
TeX (checked):
\left({\frac {\partial {{v}^{\beta }}}{\partial {{x}^{\alpha }}}}\right)'={{v}^{\beta }}_{,\alpha }'={\frac {\partial v{{'}^{\beta }}}{\partial x{{'}^{\alpha }}}}={\frac {\partial }{\partial x{{'}^{\alpha }}}}\left(\Lambda _{\sigma }^{\beta }{{v}^{\sigma }}\right)=\Lambda _{\sigma }^{\beta }{\frac {\partial {{v}^{\sigma }}}{\partial x{{'}^{\alpha }}}}=\Lambda _{\sigma }^{\beta }{\frac {\partial {{v}^{\sigma }}}{\partial {{x}^{\rho }}}}{\frac {\partial {{x}^{\rho }}}{\partial x{{'}^{\alpha }}}}=\Lambda _{\sigma }^{\beta }{\bar {\Lambda }}_{\alpha }^{\rho }{\frac {\partial {{v}^{\sigma }}}{\partial {{x}^{\rho }}}}
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MathML (4.313 KB / 433 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>v</mi><mrow data-mjx-texclass="ORD"><mi>β</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup></mrow></mrow></mfrac></mrow><mo>′</mo></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>′</mo></msup><mo>=</mo><msup><msub><msup><mi>v</mi><mrow data-mjx-texclass="ORD"><mi>β</mi></mrow></msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mo>,</mo><mo>′</mo></msup><mi>α</mi></mrow></mrow></msub><mo>′</mo></msup><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>v</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>β</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup></mrow></mrow></mfrac></mrow><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>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mrow data-mjx-texclass="ORD"><mi>σ</mi></mrow><mrow data-mjx-texclass="ORD"><mi>β</mi></mrow></msubsup><msup><mi>v</mi><mrow data-mjx-texclass="ORD"><mi>σ</mi></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msubsup><mi mathvariant="normal">Λ</mi><mrow data-mjx-texclass="ORD"><mi>σ</mi></mrow><mrow data-mjx-texclass="ORD"><mi>β</mi></mrow></msubsup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>v</mi><mrow data-mjx-texclass="ORD"><mi>σ</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup></mrow></mrow></mfrac></mrow><mo>=</mo><msubsup><mi mathvariant="normal">Λ</mi><mrow data-mjx-texclass="ORD"><mi>σ</mi></mrow><mrow data-mjx-texclass="ORD"><mi>β</mi></mrow></msubsup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>v</mi><mrow data-mjx-texclass="ORD"><mi>σ</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>ρ</mi></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>ρ</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup></mrow></mrow></mfrac></mrow><mo>=</mo><msubsup><mi mathvariant="normal">Λ</mi><mrow data-mjx-texclass="ORD"><mi>σ</mi></mrow><mrow data-mjx-texclass="ORD"><mi>β</mi></mrow></msubsup><msubsup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi mathvariant="normal">Λ</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow><mrow data-mjx-texclass="ORD"><mi>ρ</mi></mrow></msubsup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>v</mi><mrow data-mjx-texclass="ORD"><mi>σ</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>ρ</mi></mrow></msup></mrow></mrow></mfrac></mrow></mstyle></mrow></math>
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