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Display information for equation id:math.2555.52 on revision:2555

* Page found: Das ideale Fermigas (eq math.2555.52)

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Das ideale Fermigas Eq: math.2555.52

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TeX (original user input):

\begin{align}

& \Gamma \left( s+1 \right){{F}_{s}}\left( \eta  \right)\approx \frac{{{\left( \eta  \right)}^{s+1}}}{s+1}+\frac{s}{2}{{\left( \eta  \right)}^{s-1}}\frac{{{\pi }^{2}}}{3} \\

& \Gamma \left( s+1 \right){{F}_{s}}\left( \eta  \right)=\frac{{{\left( \eta  \right)}^{s+1}}}{s+1}+\frac{s}{2}{{\left( \eta  \right)}^{s-1}}\frac{{{\pi }^{2}}}{3}+O\left( {{\left( \eta  \right)}^{s-3}} \right) \\

& \Rightarrow {{F}_{s}}\left( \eta  \right)=\frac{1}{\Gamma \left( s+1 \right)}\left[ \frac{{{\left( \eta  \right)}^{s+1}}}{s+1}+\frac{s{{\pi }^{2}}}{6}{{\left( \eta  \right)}^{s-1}}+O\left( {{\left( \eta  \right)}^{s-3}} \right) \right] \\

\end{align}

TeX (checked):

{\begin{aligned}&\Gamma \left(s+1\right){{F}_{s}}\left(\eta \right)\approx {\frac {{\left(\eta \right)}^{s+1}}{s+1}}+{\frac {s}{2}}{{\left(\eta \right)}^{s-1}}{\frac {{\pi }^{2}}{3}}\\&\Gamma \left(s+1\right){{F}_{s}}\left(\eta \right)={\frac {{\left(\eta \right)}^{s+1}}{s+1}}+{\frac {s}{2}}{{\left(\eta \right)}^{s-1}}{\frac {{\pi }^{2}}{3}}+O\left({{\left(\eta \right)}^{s-3}}\right)\\&\Rightarrow {{F}_{s}}\left(\eta \right)={\frac {1}{\Gamma \left(s+1\right)}}\left[{\frac {{\left(\eta \right)}^{s+1}}{s+1}}+{\frac {s{{\pi }^{2}}}{6}}{{\left(\eta \right)}^{s-1}}+O\left({{\left(\eta \right)}^{s-3}}\right)\right]\\\end{aligned}}

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\begin{aligned} Γ (s + 1) F_{s} (η) \approx \frac{{(η)}^{s + 1}}{s + 1} + \frac{s}{2} {(η)}^{s - 1} \frac{π^{2}}{3} \\ Γ (s + 1) F_{s} (η) = \frac{{(η)}^{s + 1}}{s + 1} + \frac{s}{2} {(η)}^{s - 1} \frac{π^{2}}{3} + O ({(η)}^{s - 3}) \\ \Rightarrow F_{s} (η) = \frac{1}{Γ (s + 1)} [\frac{{(η)}^{s + 1}}{s + 1} + \frac{s π^{2}}{6} {(η)}^{s - 1} + O ({(η)}^{s - 3})] \end{aligned}

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Identifiers

$Γ$

$s$

$F_{s}$

$η$

$η$

$s$

$s$

$s$

$η$

$s$

$π$

$Γ$

$s$

$F_{s}$

$η$

$η$

$s$

$s$

$s$

$η$

$s$

$π$

$O$

$η$

$s$

$F_{s}$

$η$

$Γ$

$s$

$η$

$s$

$s$

$s$

$π$

$η$

$s$

$O$

$η$

$s$

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