Zur Navigation springen Zur Suche springen

General

Display information for equation id:math.1970.8 on revision:1970

* Page found: Der Satz von Liouville (eq math.1970.8)

(force rerendering)

Occurrences on the following pages:

Hash: 5143c0a3acf4f9fe71387760b0e03e92

TeX (original user input):

{{V}_{t}}=\int\limits_{{{U}_{t}}}^{{}}{{{d}^{2f}}{{x}_{0}}}=\int\limits_{{{U}_{{{t}_{0}}}}}^{{}}{{{d}^{2f}}{{x}_{0}}}\det \left( \frac{\partial x}{\partial {{x}_{0}}} \right)=\int\limits_{{{U}_{{{t}_{0}}}}}^{{}}{{{d}^{2f}}{{x}_{0}}}\det \left( D{{\Phi }_{t,{{t}_{0}}}}({{{\bar{x}}}_{0}}) \right)

TeX (checked):

{{V}_{t}}=\int \limits _{{U}_{t}}^{}{{{d}^{2f}}{{x}_{0}}}=\int \limits _{{U}_{{t}_{0}}}^{}{{{d}^{2f}}{{x}_{0}}}\det \left({\frac {\partial x}{\partial {{x}_{0}}}}\right)=\int \limits _{{U}_{{t}_{0}}}^{}{{{d}^{2f}}{{x}_{0}}}\det \left(D{{\Phi }_{t,{{t}_{0}}}}({{\bar {x}}_{0}})\right)

LaTeXML (experimentell; verwendet MathML) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimentell; keine Bilder) rendering

MathML (2.682 KB / 448 B) :

Vt=Utd2fx0=Ut0d2fx0det(xx0)=Ut0d2fx0det(DΦt,t0(x¯0))
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>V</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub></mstyle><mo>=</mo><munderover><mo form="prefix" texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><msub><mi>U</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>f</mi></mrow></mrow></msup><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow><mo>=</mo><munderover><mo form="prefix" texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><msub><mi>U</mi><mrow data-mjx-texclass="ORD"><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></msub></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>f</mi></mrow></mrow></msup><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow><mi>det</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>x</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><munderover><mo form="prefix" texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><msub><mi>U</mi><mrow data-mjx-texclass="ORD"><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></msub></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>f</mi></mrow></mrow></msup><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow><mi>det</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>D</mi><msub><mi mathvariant="normal">&#x03A6;</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></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Der Satz von Liouville page

Identifiers

  • Vt
  • Ut
  • f
  • x0
  • Ut0
  • f
  • x0
  • x
  • x0
  • Ut0
  • f
  • x0
  • D
  • Φt,t0
  • x¯0

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results