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Display information for equation id:math.2441.70 on revision:2441
* Page found: Spezielle Verteilungen (eq math.2441.70)
(force rerendering)Occurrences on the following pages:
Hash: 629d4c2011d6c1048a1fe23b4fef1164
TeX (original user input):
\begin{align}
& S=-k\int_{\Delta \Omega }^{{}}{d\xi }\rho \ln \rho =-k\int_{\Delta \Omega }^{{}}{d\xi }\frac{1}{\Delta \Omega }\ln \frac{1}{\Delta \Omega } \\
& \int_{\Delta \Omega }^{{}}{d\xi }\frac{1}{\Delta \Omega }=1 \\
& \Rightarrow S=k\ln \Delta \Omega \\
\end{align}
TeX (checked):
{\begin{aligned}&S=-k\int _{\Delta \Omega }^{}{d\xi }\rho \ln \rho =-k\int _{\Delta \Omega }^{}{d\xi }{\frac {1}{\Delta \Omega }}\ln {\frac {1}{\Delta \Omega }}\\&\int _{\Delta \Omega }^{}{d\xi }{\frac {1}{\Delta \Omega }}=1\\&\Rightarrow S=k\ln \Delta \Omega \\\end{aligned}}
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MathML (2.632 KB / 418 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><mi>S</mi><mo>=</mo><mo>−</mo><mi>k</mi><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">Δ</mi><mi mathvariant="normal">Ω</mi></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>ξ</mi></mrow><mi>ρ</mi><mi>ln</mi><mo>⁡</mo><mi>ρ</mi><mo>=</mo><mo>−</mo><mi>k</mi><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">Δ</mi><mi mathvariant="normal">Ω</mi></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>ξ</mi></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">Δ</mi><mi mathvariant="normal">Ω</mi></mrow></mrow></mfrac></mrow><mi>ln</mi><mo>⁡</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">Δ</mi><mi mathvariant="normal">Ω</mi></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">Δ</mi><mi mathvariant="normal">Ω</mi></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>ξ</mi></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">Δ</mi><mi mathvariant="normal">Ω</mi></mrow></mrow></mfrac></mrow><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><mi>S</mi><mo>=</mo><mi>k</mi><mi>ln</mi><mo>⁡</mo><mi mathvariant="normal">Δ</mi><mi mathvariant="normal">Ω</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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