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Display information for equation id:math.1970.9 on revision:1970
* Page found: Der Satz von Liouville (eq math.1970.9)
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Hash: 69670885cb51e3187fd8e8597c8ec951
TeX (original user input):
{{\left( D{{\Phi }_{t,{{t}_{0}}}}({{{\bar{x}}}_{0}}) \right)}_{ik}}:=\frac{\partial {{\Phi }^{i}}_{t,{{t}_{0}}}({{{\bar{x}}}_{0}})}{\partial {{x}_{0}}^{k}}=\frac{\partial {{x}^{i}}}{\partial {{x}_{0}}^{k}}
TeX (checked):
{{\left(D{{\Phi }_{t,{{t}_{0}}}}({{\bar {x}}_{0}})\right)}_{ik}}:={\frac {\partial {{\Phi }^{i}}_{t,{{t}_{0}}}({{\bar {x}}_{0}})}{\partial {{x}_{0}}^{k}}}={\frac {\partial {{x}^{i}}}{\partial {{x}_{0}}^{k}}}
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<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>D</mi><msub><mi mathvariant="normal">Φ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>t</mi><mo>,</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></msub><mo stretchy="false">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>k</mi></mrow></mrow></msub></mstyle><mi>:</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><msup><mi mathvariant="normal">Φ</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>t</mi><mo>,</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></msub><mo stretchy="false">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msup></mrow></mrow></mfrac></mrow><mo>=</mo><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>i</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msup></mrow></mrow></mfrac></mrow></mrow></math>
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