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Display information for equation id:math.940.54 on revision:940
* Page found: Verallgemeinerte kanonische Verteilung (eq math.940.54)
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Hash: 7582a99a5db2e5e8bb8a27bf5f53f1d6
TeX (original user input):
\begin{align}
& I(P)=\sum\limits_{i}^{{}}{{}}{{P}_{i}}\ln {{P}_{i}}=\sum\limits_{i}^{{}}{{}}{{P}_{i}}\left( \Psi -{{\lambda }_{n}}{{M}_{i}}^{n} \right)=\Psi -{{\lambda }_{n}}\sum\limits_{i}^{{}}{{}}{{P}_{i}}{{M}_{i}}^{n} \\
& I=\Psi \left( {{\lambda }_{1}},...{{\lambda }_{m}} \right)-{{\lambda }_{n}}\left\langle {{M}^{n}} \right\rangle \\
\end{align}
TeX (checked):
{\begin{aligned}&I(P)=\sum \limits _{i}^{}{}{{P}_{i}}\ln {{P}_{i}}=\sum \limits _{i}^{}{}{{P}_{i}}\left(\Psi -{{\lambda }_{n}}{{M}_{i}}^{n}\right)=\Psi -{{\lambda }_{n}}\sum \limits _{i}^{}{}{{P}_{i}}{{M}_{i}}^{n}\\&I=\Psi \left({{\lambda }_{1}},...{{\lambda }_{m}}\right)-{{\lambda }_{n}}\left\langle {{M}^{n}}\right\rangle \\\end{aligned}}
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MathML (2.586 KB / 488 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>I</mi><mo stretchy="false">(</mo><mi>P</mi><mo stretchy="false">)</mo><mo>=</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mi>ln</mi><mo>⁡</mo><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo>=</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">Ψ</mi><mo>−</mo><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>n</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>=</mo><mi mathvariant="normal">Ψ</mi><mo>−</mo><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><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></mtd></mtr><mtr><mtd></mtd><mtd><mi>I</mi><mo>=</mo><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>−</mo><msub><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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