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Das ideale Bosegas Eq: math.2561.13

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TeX (original user input):

\begin{align}
  & \bar{N}=\sum\limits_{j}^{{}}{{}}\left\langle {{N}_{j}} \right\rangle \approx \left( 2s+1 \right)\frac{4\pi V}{{{h}^{3}}}\int_{0}^{\infty }{{}}dp{{p}^{2}}\frac{1}{\exp \left( \frac{\left( {{E}_{j}}-\mu  \right)}{kT} \right)-1}=\left( 2s+1 \right)\frac{4\pi V}{{{h}^{3}}}\int_{0}^{\infty }{{}}dp{{p}^{2}}\frac{1}{\exp \left( \frac{\left( \frac{{{p}^{2}}}{2m}-\mu  \right)}{kT} \right)-1} \\ 
 & \frac{{{p}^{2}}}{2mkT}=y \\ 
 & \Rightarrow \bar{N}=\sum\limits_{j}^{{}}{{}}\left\langle {{N}_{j}} \right\rangle \approx \left( 2s+1 \right)\frac{4\pi V}{{{h}^{3}}}\int_{0}^{\infty }{{}}dp{{p}^{2}}\frac{1}{\exp \left( \frac{\left( \frac{{{p}^{2}}}{2m}-\mu  \right)}{kT} \right)-1} \\  
 & =\frac{\left( 2s+1 \right)}{2}\frac{4\pi V}{{{h}^{3}}}{{\left( 2mkT \right)}^{\frac{3}{2}}}\int_{0}^{\infty }{{}}dy\frac{{{y}^{\frac{1}{2}}}}{{{\xi }^{-1}}\exp \left( y \right)-1}=\frac{\left( 2s+1 \right)}{2}\frac{4\pi V}{{{h}^{3}}}{{\left( 2mkT \right)}^{\frac{3}{2}}}\int_{0}^{\infty }{{}}dy{{y}^{\frac{1}{2}}}\frac{\xi {{e}^{-y}}}{1-\xi {{e}^{-y}}} \\ 
 & \int_{0}^{\infty }{{}}dy{{y}^{\frac{1}{2}}}\frac{\xi {{e}^{-y}}}{1-\xi {{e}^{-y}}}\approx \xi \int_{0}^{\infty }{{}}dy{{y}^{\frac{1}{2}}}{{e}^{-y}}+{{\xi }^{2}}\int_{0}^{\infty }{{}}dy{{y}^{\frac{1}{2}}}{{e}^{-2y}}+.... \\ 
 & \int_{0}^{\infty }{{}}dy{{y}^{\frac{1}{2}}}{{e}^{-y}}=\frac{1}{2}\sqrt{\pi } \\ 
 & \int_{0}^{\infty }{{}}dy{{y}^{\frac{1}{2}}}{{e}^{-2y}}=\frac{1}{{{2}^{\frac{5}{2}}}}\sqrt{\pi } \\ 
 & \Rightarrow \bar{N}\approx \frac{\left( 2s+1 \right)}{4}\frac{4V}{{{h}^{3}}}{{\left( 2\pi mkT \right)}^{\frac{3}{2}}}\left[ \xi +\frac{1}{{{2}^{\frac{3}{2}}}}{{\xi }^{2}} \right] \\ 
 & \lambda :={{\left( \frac{{{h}^{2}}}{2\pi mkT} \right)}^{\frac{1}{2}}}={{\left( \frac{2s+1}{{{N}_{C}}} \right)}^{\frac{1}{3}}} \\ 
 & \Rightarrow \bar{N}\approx \left( 2s+1 \right)\frac{V}{{{\lambda }^{3}}}\xi \left[ 1+\frac{1}{{{2}^{\frac{3}{2}}}}\xi  \right]=\left( 2s+1 \right)\frac{V}{{{\lambda }^{3}}}{{e}^{\frac{\mu }{kT}}}\left[ 1+\frac{1}{{{2}^{\frac{3}{2}}}}{{e}^{\frac{\mu }{kT}}} \right] \\ 
\end{align}

TeX (checked):

{\begin{aligned}&{\bar {N}}=\sum \limits _{j}^{}{}\left\langle {{N}_{j}}\right\rangle \approx \left(2s+1\right){\frac {4\pi V}{{h}^{3}}}\int _{0}^{\infty }{}dp{{p}^{2}}{\frac {1}{\exp \left({\frac {\left({{E}_{j}}-\mu \right)}{kT}}\right)-1}}=\left(2s+1\right){\frac {4\pi V}{{h}^{3}}}\int _{0}^{\infty }{}dp{{p}^{2}}{\frac {1}{\exp \left({\frac {\left({\frac {{p}^{2}}{2m}}-\mu \right)}{kT}}\right)-1}}\\&{\frac {{p}^{2}}{2mkT}}=y\\&\Rightarrow {\bar {N}}=\sum \limits _{j}^{}{}\left\langle {{N}_{j}}\right\rangle \approx \left(2s+1\right){\frac {4\pi V}{{h}^{3}}}\int _{0}^{\infty }{}dp{{p}^{2}}{\frac {1}{\exp \left({\frac {\left({\frac {{p}^{2}}{2m}}-\mu \right)}{kT}}\right)-1}}\\&={\frac {\left(2s+1\right)}{2}}{\frac {4\pi V}{{h}^{3}}}{{\left(2mkT\right)}^{\frac {3}{2}}}\int _{0}^{\infty }{}dy{\frac {{y}^{\frac {1}{2}}}{{{\xi }^{-1}}\exp \left(y\right)-1}}={\frac {\left(2s+1\right)}{2}}{\frac {4\pi V}{{h}^{3}}}{{\left(2mkT\right)}^{\frac {3}{2}}}\int _{0}^{\infty }{}dy{{y}^{\frac {1}{2}}}{\frac {\xi {{e}^{-y}}}{1-\xi {{e}^{-y}}}}\\&\int _{0}^{\infty }{}dy{{y}^{\frac {1}{2}}}{\frac {\xi {{e}^{-y}}}{1-\xi {{e}^{-y}}}}\approx \xi \int _{0}^{\infty }{}dy{{y}^{\frac {1}{2}}}{{e}^{-y}}+{{\xi }^{2}}\int _{0}^{\infty }{}dy{{y}^{\frac {1}{2}}}{{e}^{-2y}}+....\\&\int _{0}^{\infty }{}dy{{y}^{\frac {1}{2}}}{{e}^{-y}}={\frac {1}{2}}{\sqrt {\pi }}\\&\int _{0}^{\infty }{}dy{{y}^{\frac {1}{2}}}{{e}^{-2y}}={\frac {1}{{2}^{\frac {5}{2}}}}{\sqrt {\pi }}\\&\Rightarrow {\bar {N}}\approx {\frac {\left(2s+1\right)}{4}}{\frac {4V}{{h}^{3}}}{{\left(2\pi mkT\right)}^{\frac {3}{2}}}\left[\xi +{\frac {1}{{2}^{\frac {3}{2}}}}{{\xi }^{2}}\right]\\&\lambda :={{\left({\frac {{h}^{2}}{2\pi mkT}}\right)}^{\frac {1}{2}}}={{\left({\frac {2s+1}{{N}_{C}}}\right)}^{\frac {1}{3}}}\\&\Rightarrow {\bar {N}}\approx \left(2s+1\right){\frac {V}{{\lambda }^{3}}}\xi \left[1+{\frac {1}{{2}^{\frac {3}{2}}}}\xi \right]=\left(2s+1\right){\frac {V}{{\lambda }^{3}}}{{e}^{\frac {\mu }{kT}}}\left[1+{\frac {1}{{2}^{\frac {3}{2}}}}{{e}^{\frac {\mu }{kT}}}\right]\\\end{aligned}}

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\begin{aligned} \bar{N} = \sum_{j}^{} ⟨ N_{j} ⟩ \approx (2 s + 1) \frac{4 π V}{h^{3}} \int_{0}^{\infty} d p p^{2} \frac{1}{\exp (\frac{(E_{j} - μ)}{k T}) - 1} = (2 s + 1) \frac{4 π V}{h^{3}} \int_{0}^{\infty} d p p^{2} \frac{1}{\exp (\frac{(\frac{p^{2}}{2 m} - μ)}{k T}) - 1} \\ \frac{p^{2}}{2 m k T} = y \\ \Rightarrow \bar{N} = \sum_{j}^{} ⟨ N_{j} ⟩ \approx (2 s + 1) \frac{4 π V}{h^{3}} \int_{0}^{\infty} d p p^{2} \frac{1}{\exp (\frac{(\frac{p^{2}}{2 m} - μ)}{k T}) - 1} \\ = \frac{(2 s + 1)}{2} \frac{4 π V}{h^{3}} {(2 m k T)}^{\frac{3}{2}} \int_{0}^{\infty} d y \frac{y^{\frac{1}{2}}}{ξ^{- 1} \exp (y) - 1} = \frac{(2 s + 1)}{2} \frac{4 π V}{h^{3}} {(2 m k T)}^{\frac{3}{2}} \int_{0}^{\infty} d y y^{\frac{1}{2}} \frac{ξ e^{- y}}{1 - ξ e^{- y}} \\ \int_{0}^{\infty} d y y^{\frac{1}{2}} \frac{ξ e^{- y}}{1 - ξ e^{- y}} \approx ξ \int_{0}^{\infty} d y y^{\frac{1}{2}} e^{- y} + ξ^{2} \int_{0}^{\infty} d y y^{\frac{1}{2}} e^{- 2 y} + . . . . \\ \int_{0}^{\infty} d y y^{\frac{1}{2}} e^{- y} = \frac{1}{2} \sqrt{π} \\ \int_{0}^{\infty} d y y^{\frac{1}{2}} e^{- 2 y} = \frac{1}{2^{\frac{5}{2}}} \sqrt{π} \\ \Rightarrow \bar{N} \approx \frac{(2 s + 1)}{4} \frac{4 V}{h^{3}} {(2 π m k T)}^{\frac{3}{2}} [ξ + \frac{1}{2^{\frac{3}{2}}} ξ^{2}] \\ λ : = {(\frac{h^{2}}{2 π m k T})}^{\frac{1}{2}} = {(\frac{2 s + 1}{N_{C}})}^{\frac{1}{3}} \\ \Rightarrow \bar{N} \approx (2 s + 1) \frac{V}{λ^{3}} ξ [1 + \frac{1}{2^{\frac{3}{2}}} ξ] = (2 s + 1) \frac{V}{λ^{3}} e^{\frac{μ}{k T}} [1 + \frac{1}{2^{\frac{3}{2}}} e^{\frac{μ}{k T}}] \end{aligned}

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data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></msup><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mi>y</mi></mrow></mrow></msup><mo>+</mo><msup><mi>&#x03BE;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">&#x221E;</mi></mrow></munderover></mstyle><mi>d</mi><mi>y</mi><msup><mi>y</mi><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"><mn>2</mn></mrow></mfrac></mrow></mrow></msup><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mn>2</mn><mi>y</mi></mrow></mrow></msup><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo></mtd></mtr><mtr><mtd></mtd><mtd><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">&#x221E;</mi></mrow></munderover></mstyle><mi>d</mi><mi>y</mi><msup><mi>y</mi><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"><mn>2</mn></mrow></mfrac></mrow></mrow></msup><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mi>y</mi></mrow></mrow></msup><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><msqrt><mi>&#x03C0;</mi></msqrt></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">&#x221E;</mi></mrow></munderover></mstyle><mi>d</mi><mi>y</mi><msup><mi>y</mi><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"><mn>2</mn></mrow></mfrac></mrow></mrow></msup><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mn>2</mn><mi>y</mi></mrow></mrow></msup><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mn>2</mn><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>5</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></msup></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><msqrt><mi>&#x03C0;</mi></msqrt></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>&#x21D2;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>N</mi><mo>¯</mo></mover></mrow></mrow><mo>&#x2248;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><mi>s</mi><mo>+</mo><mn>1</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>V</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><msup><mi>h</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mfrac></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><mi>&#x03C0;</mi><mi>m</mi><mi>k</mi><mi>T</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mi>&#x03BE;</mi><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mn>2</mn><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></msup></mrow></mfrac></mrow><msup><mi>&#x03BE;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">]</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>&#x03BB;</mi><mi>:</mi><mo>=</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>h</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>&#x03C0;</mi><mi>m</mi><mi>k</mi><mi>T</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><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"><mn>2</mn></mrow></mfrac></mrow></mrow></msup><mo>=</mo><msup><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"><mn>2</mn><mi>s</mi><mo>+</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mi>C</mi></mrow></msub></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><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"><mn>3</mn></mrow></mfrac></mrow></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo>&#x21D2;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>N</mi><mo>¯</mo></mover></mrow></mrow><mo>&#x2248;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><mi>s</mi><mo>+</mo><mn>1</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"><msup><mi>&#x03BB;</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mfrac></mrow><mi>&#x03BE;</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mn>1</mn><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mn>2</mn><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></msup></mrow></mfrac></mrow><mi>&#x03BE;</mi><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><mi>s</mi><mo>+</mo><mn>1</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"><msup><mi>&#x03BB;</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mfrac></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>&#x03BC;</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mi>T</mi></mrow></mrow></mfrac></mrow></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mn>1</mn><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mn>2</mn><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></msup></mrow></mfrac></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>&#x03BC;</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mi>T</mi></mrow></mrow></mfrac></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">]</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$\bar{N}$

$j$

$N_{j}$

$s$

$π$

$V$

$h$

$p$

$p$

$E_{j}$

$μ$

$k$

$T$

$s$

$π$

$V$

$h$

$p$

$p$

$p$

$m$

$μ$

$k$

$T$

$p$

$m$

$k$

$T$

$y$

$\bar{N}$

$j$

$N_{j}$

$s$

$π$

$V$

$h$

$p$

$p$

$p$

$m$

$μ$

$k$

$T$

$s$

$π$

$V$

$h$

$m$

$k$

$T$

$y$

$y$

$ξ$

$y$

$s$

$π$

$V$

$h$

$m$

$k$

$T$

$y$

$y$

$ξ$

$e$

$y$

$ξ$

$e$

$y$

$y$

$y$

$ξ$

$e$

$y$

$ξ$

$e$

$y$

$ξ$

$y$

$y$

$e$

$y$

$ξ$

$y$

$y$

$e$

$y$

$y$

$y$

$e$

$y$

$π$

$y$

$y$

$e$

$y$

$π$

$\bar{N}$

$s$

$V$

$h$

$π$

$m$

$k$

$T$

$ξ$

$ξ$

$λ$

$h$

$π$

$m$

$k$

$T$

$s$

$N_{C}$

$\bar{N}$

$s$

$V$

$λ$

$ξ$

$ξ$

$s$

$V$

$λ$

$e$

$μ$

$k$

$T$

$e$

$μ$

$k$

$T$

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LaTeXML (experimentell; verwendet MathML) rendering

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Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

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General

LaTeXML (experimentell; verwendet MathML) rendering

MathML (experimentell; keine Bilder) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigationsmenü

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