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Display information for equation id:math.1970.11 on revision:1970
* Page found: Der Satz von Liouville (eq math.1970.11)
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Hash: 5299cf6e49edfbef5bec0dbaad57b4a5
TeX (original user input):
\frac{\partial {{\Phi }^{i}}_{t,{{t}_{0}}}({{{\bar{x}}}_{0}})}{\partial {{x}_{0}}^{k}}={{\delta }_{ik}}+\frac{\partial {{{\bar{F}}}^{i}}({{{\bar{x}}}_{0}},t)}{\partial {{x}_{0}}^{k}}(t-{{t}_{0}})+O({{(t-{{t}_{0}})}^{2}})
TeX (checked):
{\frac {\partial {{\Phi }^{i}}_{t,{{t}_{0}}}({{\bar {x}}_{0}})}{\partial {{x}_{0}}^{k}}}={{\delta }_{ik}}+{\frac {\partial {{\bar {F}}^{i}}({{\bar {x}}_{0}},t)}{\partial {{x}_{0}}^{k}}}(t-{{t}_{0}})+O({{(t-{{t}_{0}})}^{2}})
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MathML (2.372 KB / 407 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"><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><msub><mi>δ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>k</mi></mrow></mrow></msub><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>F</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msup><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>,</mo><mi>t</mi><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 stretchy="false">(</mo><mi>t</mi><mo>−</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><mi>O</mi><mo stretchy="false">(</mo><msup><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>t</mi><mo>−</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">)</mo></mstyle></mrow></math>
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