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Display information for equation id:math.2561.3 on revision:2561
* Page found: Das ideale Bosegas (eq math.2561.3)
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TeX (original user input):
\begin{align}
& P\left( {{N}_{1}},{{N}_{2}},... \right)={{Y}^{-1}}\exp \left( -\beta \left( {{N}_{j}}{{E}_{j}}-\mu {{N}_{j}} \right) \right)=\prod\limits_{j=1}^{l}{{}}\left( 1-{{t}_{j}} \right){{t}_{j}}^{{{N}_{j}}}=\prod\limits_{j=1}^{l}{{}}p\left( {{N}_{j}} \right) \\
& (separiert) \\
& \\
& p\left( {{N}_{j}} \right)=\left( 1-{{t}_{j}} \right){{t}_{j}}^{{{N}_{j}}}=\left( 1-\exp \left( \beta \left( \mu -{{E}_{j}} \right) \right) \right)\exp \left( -\beta \left( {{N}_{j}}{{E}_{j}}-\mu {{N}_{j}} \right) \right) \\
& 1-\exp \left( \beta \left( \mu -{{E}_{j}} \right) \right):={{e}^{{{\Psi }_{j}}}} \\
& p\left( {{N}_{j}} \right)={{e}^{{{\Psi }_{j}}}}\exp \left( -\beta \left( {{N}_{j}}{{E}_{j}}-\mu {{N}_{j}} \right) \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&P\left({{N}_{1}},{{N}_{2}},...\right)={{Y}^{-1}}\exp \left(-\beta \left({{N}_{j}}{{E}_{j}}-\mu {{N}_{j}}\right)\right)=\prod \limits _{j=1}^{l}{}\left(1-{{t}_{j}}\right){{t}_{j}}^{{N}_{j}}=\prod \limits _{j=1}^{l}{}p\left({{N}_{j}}\right)\\&(separiert)\\&\\&p\left({{N}_{j}}\right)=\left(1-{{t}_{j}}\right){{t}_{j}}^{{N}_{j}}=\left(1-\exp \left(\beta \left(\mu -{{E}_{j}}\right)\right)\right)\exp \left(-\beta \left({{N}_{j}}{{E}_{j}}-\mu {{N}_{j}}\right)\right)\\&1-\exp \left(\beta \left(\mu -{{E}_{j}}\right)\right):={{e}^{{\Psi }_{j}}}\\&p\left({{N}_{j}}\right)={{e}^{{\Psi }_{j}}}\exp \left(-\beta \left({{N}_{j}}{{E}_{j}}-\mu {{N}_{j}}\right)\right)\\\end{aligned}}
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<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>P</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msup><mi>Y</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mn>1</mn></mrow></mrow></msup><mi>exp</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>−</mo><mi>β</mi><mrow data-mjx-texclass="INNER"><mo 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texclass="OP">∏</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>j</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></munderover><mi>p</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">(</mo><mi>s</mi><mi>e</mi><mi>p</mi><mi>a</mi><mi>r</mi><mi>i</mi><mi>e</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd></mtd></mtr><mtr><mtd></mtd><mtd><mi>p</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo>−</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo 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data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo>−</mo><mi>μ</mi><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mn>1</mn><mo>−</mo><mi>exp</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>β</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>μ</mi><mo>−</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>:</mi><mo>=</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mi>p</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo 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