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Display information for equation id:math.2441.15 on revision:2441

* Page found: Spezielle Verteilungen (eq math.2441.15)

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Spezielle Verteilungen Eq: math.2441.15

Hash: 0e1b6b4c0bd62a44846304d1f788c9de

TeX (original user input):

\begin{align}

& S(U,V)=k\left[ \beta \left( U+pV \right)-\Psi \left( T,p \right) \right] \\

& mit \\

& \beta =\beta \left( U,V \right)=\frac{1}{kT} \\

& p=p\left( U,V \right) \\

& {{\left( \frac{\partial \Psi }{\partial \beta } \right)}_{p}}=U \\

& {{\left( \frac{\partial \Psi }{\partial \left( \frac{p}{kT} \right)} \right)}_{\beta }}=V \\

\end{align}

TeX (checked):

{\begin{aligned}&S(U,V)=k\left[\beta \left(U+pV\right)-\Psi \left(T,p\right)\right]\\&mit\\&\beta =\beta \left(U,V\right)={\frac {1}{kT}}\\&p=p\left(U,V\right)\\&{{\left({\frac {\partial \Psi }{\partial \beta }}\right)}_{p}}=U\\&{{\left({\frac {\partial \Psi }{\partial \left({\frac {p}{kT}}\right)}}\right)}_{\beta }}=V\\\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

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MathML (experimentell; keine Bilder) rendering

MathML (2.975 KB / 512 B) :

\begin{aligned} S (U, V) = k [β (U + p V) - Ψ (T, p)] \\ m i t \\ β = β (U, V) = \frac{1}{k T} \\ p = p (U, V) \\ {(\frac{\partial Ψ}{\partial β})}_{p} = U \\ {(\frac{\partial Ψ}{\partial (\frac{p}{k T})})}_{β} = V \end{aligned}

<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 stretchy="false">(</mo><mi>U</mi><mo>,</mo><mi>V</mi><mo stretchy="false">)</mo><mo>=</mo><mi>k</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mi>&#x03B2;</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>U</mi><mo>+</mo><mi>p</mi><mi>V</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>&#x2212;</mo><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>T</mi><mo>,</mo><mi>p</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>m</mi><mi>i</mi><mi>t</mi></mtd></mtr><mtr><mtd></mtd><mtd><mi>&#x03B2;</mi><mo>=</mo><mi>&#x03B2;</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>U</mi><mo>,</mo><mi>V</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><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>k</mi><mi>T</mi></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>p</mi><mo>=</mo><mi>p</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>U</mi><mo>,</mo><mi>V</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><msub><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 mathvariant="normal">&#x03A8;</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>&#x03B2;</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>p</mi></mrow></msub><mo>=</mo><mi>U</mi></mtd></mtr><mtr><mtd></mtd><mtd><msub><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 mathvariant="normal">&#x03A8;</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>p</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mi>T</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>&#x03B2;</mi></mrow></msub><mo>=</mo><mi>V</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

Translations to Computer Algebra Systems

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In Maple:

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In Mathematica:

Identifiers

$S$

$U$

$V$

$k$

$β$

$U$

$p$

$V$

$Ψ$

$T$

$p$

$m$

$i$

$t$

$β$

$β$

$U$

$V$

$k$

$T$

$p$

$p$

$U$

$V$

$Ψ$

$β$

$p$

$U$

$Ψ$

$p$

$k$

$T$

$β$

$V$

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LaTeXML (experimentell; verwendet MathML) rendering

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Translation to Mathematica

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MathML observations

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