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Display information for equation id:math.2268.31 on revision:2268
* Page found: Vorurteilsfreie Schätzung des statistischen Operators zu einem festen Zeitpunkt (eq math.2268.31)
(force rerendering)Occurrences on the following pages:
Hash: 8d1ff20c92d7f6ddd71e8a87bd8f7f00
TeX (original user input):
\begin{align}
& \eta \left( {{\rho }_{d}} \right)=-k\sum\limits_{i=1}^{d}{\left\langle i \right|}\frac{1}{d}\ln \frac{1}{d}\left| i \right\rangle \\
& =k\sum\limits_{i=1}^{d}{\frac{1}{d}\ln \frac{1}{d}}=k\ln \frac{1}{d}
\end{align}
TeX (checked):
{\begin{aligned}&\eta \left({{\rho }_{d}}\right)=-k\sum \limits _{i=1}^{d}{\left\langle i\right|}{\frac {1}{d}}\ln {\frac {1}{d}}\left|i\right\rangle \\&=k\sum \limits _{i=1}^{d}{{\frac {1}{d}}\ln {\frac {1}{d}}}=k\ln {\frac {1}{d}}\end{aligned}}
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MathML (2.242 KB / 444 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>η</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>ρ</mi><mrow data-mjx-texclass="ORD"><mi>d</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mo>−</mo><mi>k</mi><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>d</mi></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>i</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>d</mi></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"><mi>d</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>i</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mi>k</mi><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>d</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>d</mi></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"><mi>d</mi></mrow></mfrac></mrow></mrow><mo>=</mo><mi>k</mi><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"><mi>d</mi></mrow></mfrac></mrow></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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