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Display information for equation id:math.940.101 on revision:940

* Page found: Verallgemeinerte kanonische Verteilung (eq math.940.101)

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Verallgemeinerte kanonische Verteilung Eq: math.940.101

Hash: 135fc3ec538900fc932e85f402459cb1

TeX (original user input):

\begin{align}
  & K\left( P,{{P}^{0}} \right)=I(P)-I({{P}^{0}})+{{\lambda }_{n}}\left( \sum\limits_{i}^{{}}{{}}\left( {{P}_{i}}{{M}_{i}}^{n} \right)-\sum\limits_{i}^{{}}{{}}\left( {{P}_{i}}^{0}{{M}_{i}}^{n} \right) \right) \\
 & =I(P)-I({{P}^{0}})+{{\lambda }_{n}}\left( \left\langle {{M}^{n}} \right\rangle -{{\left\langle {{M}^{n}} \right\rangle }_{0}} \right) \\ 
 & keine\ddot{A}nderung \\ 
 & \Rightarrow {{\lambda }_{n}}\left( \left\langle {{M}^{n}} \right\rangle -{{\left\langle {{M}^{n}} \right\rangle }_{0}} \right)=0 \\ 
 & \left\langle {{M}^{n}} \right\rangle ={{\left\langle {{M}^{n}} \right\rangle }_{0}} \\ 
\end{align}

TeX (checked):

{\begin{aligned}&K\left(P,{{P}^{0}}\right)=I(P)-I({{P}^{0}})+{{\lambda }_{n}}\left(\sum \limits _{i}^{}{}\left({{P}_{i}}{{M}_{i}}^{n}\right)-\sum \limits _{i}^{}{}\left({{P}_{i}}^{0}{{M}_{i}}^{n}\right)\right)\\&=I(P)-I({{P}^{0}})+{{\lambda }_{n}}\left(\left\langle {{M}^{n}}\right\rangle -{{\left\langle {{M}^{n}}\right\rangle }_{0}}\right)\\&keine{\ddot {A}}nderung\\&\Rightarrow {{\lambda }_{n}}\left(\left\langle {{M}^{n}}\right\rangle -{{\left\langle {{M}^{n}}\right\rangle }_{0}}\right)=0\\&\left\langle {{M}^{n}}\right\rangle ={{\left\langle {{M}^{n}}\right\rangle }_{0}}\\\end{aligned}}

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MathML (4.404 KB / 572 B) :

\begin{aligned} K (P, P^{0}) = I (P) - I (P^{0}) + λ_{n} (\sum_{i}^{} (P_{i} {M_{i}}^{n}) - \sum_{i}^{} ({P_{i}}^{0} {M_{i}}^{n})) \\ = I (P) - I (P^{0}) + λ_{n} (⟨ M^{n} ⟩ - {⟨ M^{n} ⟩}_{0}) \\ k e i n e \ddot{A} n d e r u n g \\ \Rightarrow λ_{n} (⟨ M^{n} ⟩ - {⟨ M^{n} ⟩}_{0}) = 0 \\ ⟨ M^{n} ⟩ = {⟨ M^{n} ⟩}_{0} \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>K</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>P</mi><mo>,</mo><msup><mi>P</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi>I</mi><mo stretchy="false">(</mo><mi>P</mi><mo stretchy="false">)</mo><mo>&#x2212;</mo><mi>I</mi><mo stretchy="false">(</mo><msup><mi>P</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo stretchy="false">)</mo><mo>+</mo><msub><mi>&#x03BB;</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><msup><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>&#x2212;</mo><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><msup><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mi>I</mi><mo stretchy="false">(</mo><mi>P</mi><mo stretchy="false">)</mo><mo>&#x2212;</mo><mi>I</mi><mo stretchy="false">(</mo><msup><mi>P</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mo stretchy="false">)</mo><mo>+</mo><msub><mi>&#x03BB;</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo>&#x2212;</mo><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>k</mi><mi>e</mi><mi>i</mi><mi>n</mi><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¨</mo></mover></mrow></mrow><mi>n</mi><mi>d</mi><mi>e</mi><mi>r</mi><mi>u</mi><mi>n</mi><mi>g</mi></mtd></mtr><mtr><mtd></mtd><mtd><mo>&#x21D2;</mo><msub><mi>&#x03BB;</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo>&#x2212;</mo><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo>=</mo><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></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

$K$

$P$

$P$

$I$

$P$

$I$

$P$

$λ_{n}$

$i$

$P_{i}$

$M_{i}$

$n$

$i$

$P_{i}$

$M_{i}$

$n$

$I$

$P$

$I$

$P$

$λ_{n}$

$M$

$n$

$M$

$n$

$k$

$e$

$i$

$n$

$e$

$\ddot{A}$

$n$

$d$

$e$

$r$

$u$

$n$

$g$

$λ_{n}$

$M$

$n$

$M$

$n$

$M$

$n$

$M$

$n$

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