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Display information for equation id:math.2555.53 on revision:2555

* Page found: Das ideale Fermigas (eq math.2555.53)

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Hash: 13ebeae762db081ecabfc0c7e3acddc9

TeX (original user input): 

\begin{align}

& {{F}_{\frac{1}{2}}}\left( \eta  \right)\approx \frac{2}{\sqrt{\pi }}\left[ \frac{{{\left( \eta  \right)}^{\frac{3}{2}}}}{\frac{3}{2}}+\frac{{{\pi }^{2}}}{12}{{\left( \eta  \right)}^{-\frac{1}{2}}} \right] \\

& {{F}_{\frac{3}{2}}}\left( \eta  \right)\approx \frac{4}{3\sqrt{\pi }}\left[ \frac{{{\left( \eta  \right)}^{\frac{5}{2}}}}{\frac{5}{2}}+\frac{{{\pi }^{2}}}{4}{{\left( \eta  \right)}^{\frac{1}{2}}} \right] \\

\end{align}

TeX (checked): 

{\begin{aligned}&{{F}_{\frac {1}{2}}}\left(\eta \right)\approx {\frac {2}{\sqrt {\pi }}}\left[{\frac {{\left(\eta \right)}^{\frac {3}{2}}}{\frac {3}{2}}}+{\frac {{\pi }^{2}}{12}}{{\left(\eta \right)}^{-{\frac {1}{2}}}}\right]\\&{{F}_{\frac {3}{2}}}\left(\eta \right)\approx {\frac {4}{3{\sqrt {\pi }}}}\left[{\frac {{\left(\eta \right)}^{\frac {5}{2}}}{\frac {5}{2}}}+{\frac {{\pi }^{2}}{4}}{{\left(\eta \right)}^{\frac {1}{2}}}\right]\\\end{aligned}}

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MathML (26.004 KB / 2.83 KB) :

F 1 2 ⁢ ( η ) ≈ 2 π ⁢ [ ( η ) 3 2 3 2 + π 2 12 ⁢ ( η ) - 1 2 ] F 3 2 ⁢ ( η ) ≈ 4 3 ⁢ π ⁢ [ ( η ) 5 2 5 2 + π 2 4 ⁢ ( η ) 1 2 ] absent subscript 𝐹 1 2 𝜂 2 𝜋 delimited-[] superscript 𝜂 3 2 3 2 superscript 𝜋 2 12 superscript 𝜂 1 2 absent subscript 𝐹 3 2 𝜂 4 3 𝜋 delimited-[] superscript 𝜂 5 2 5 2 superscript 𝜋 2 4 superscript 𝜂 1 2 {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle{{F}_{\frac{1}{2% }}}\left(\eta\right)\approx\frac{2}{\sqrt{\pi}}\left[\frac{{{\left(\eta\right)% }^{\frac{3}{2}}}}{\frac{3}{2}}+\frac{{{\pi}^{2}}}{12}{{\left(\eta\right)}^{-% \frac{1}{2}}}\right]\\ \par&\displaystyle{{F}_{\frac{3}{2}}}\left(\eta\right)\approx\frac{4}{3\sqrt{% \pi}}\left[\frac{{{\left(\eta\right)}^{\frac{5}{2}}}}{\frac{5}{2}}+\frac{{{\pi% }^{2}}}{4}{{\left(\eta\right)}^{\frac{1}{2}}}\right]\\ \par\end{aligned}}}

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MathML (4.15 KB / 461 B) :

F12(η)≈2π[(η)3232+π212(η)−12]F32(η)≈43π[(η)5252+π24(η)12]

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Calculated based on the variables occurring on the entire Das ideale Fermigas page

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Abgerufen von „https://wiki.physikerwelt.de/wiki/Spezial:Formelinformation“