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Display information for equation id:math.2433.70 on revision:2433
* Page found: Spezielle Verteilungen (eq math.2433.70)
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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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<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>S</mi><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mi>k</mi><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>Δ</mi><mi>Ω</mi></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>ξ</mi></mrow><mi>ρ</mi><mi>ln</mi><mo>⁡</mo><mi>ρ</mi><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mi>k</mi><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>Δ</mi><mi>Ω</mi></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><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>Δ</mi><mi>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>Δ</mi><mi>Ω</mi></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>Δ</mi><mi>Ω</mi></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><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>Δ</mi><mi>Ω</mi></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mn>1</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><mi>S</mi><mo stretchy="false">=</mo><mi>k</mi><mi>ln</mi><mo>⁡</mo><mi>Δ</mi><mi>Ω</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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