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Display information for equation id:math.2555.44 on revision:2555

* Page found: Das ideale Fermigas (eq math.2555.44)

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Das ideale Fermigas Eq: math.2555.44

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TeX (original user input):

\begin{align}

& x=y-\eta  \\

& \Rightarrow \Gamma \left( s+1 \right){{F}_{s}}\left( \eta  \right)=\frac{1}{s+1}\int_{0}^{\infty }{{}}dy{{y}^{s+1}}\frac{{{e}^{y-\eta }}}{{{\left( {{e}^{y-\eta }}+1 \right)}^{2}}}=\frac{1}{s+1}\int_{-\eta }^{\infty }{{}}dx{{\left( x+\eta  \right)}^{s+1}}\frac{{{e}^{x}}}{{{\left( {{e}^{x}}+1 \right)}^{2}}} \\

& \eta >>1 \\

\end{align}

TeX (checked):

{\begin{aligned}&x=y-\eta \\&\Rightarrow \Gamma \left(s+1\right){{F}_{s}}\left(\eta \right)={\frac {1}{s+1}}\int _{0}^{\infty }{}dy{{y}^{s+1}}{\frac {{e}^{y-\eta }}{{\left({{e}^{y-\eta }}+1\right)}^{2}}}={\frac {1}{s+1}}\int _{-\eta }^{\infty }{}dx{{\left(x+\eta \right)}^{s+1}}{\frac {{e}^{x}}{{\left({{e}^{x}}+1\right)}^{2}}}\\&\eta >>1\\\end{aligned}}

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\begin{aligned} x = y - η \\ \Rightarrow Γ (s + 1) F_{s} (η) = \frac{1}{s + 1} \int_{0}^{\infty} d y y^{s + 1} \frac{e^{y - η}}{{(e^{y - η} + 1)}^{2}} = \frac{1}{s + 1} \int_{- η}^{\infty} d x {(x + η)}^{s + 1} \frac{e^{x}}{{(e^{x} + 1)}^{2}} \\ η > > 1 \end{aligned}

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Identifiers

$x$

$y$

$η$

$Γ$

$s$

$F_{s}$

$η$

$s$

$y$

$y$

$s$

$e$

$y$

$η$

$e$

$y$

$η$

$s$

$η$

$x$

$x$

$η$

$s$

$e$

$x$

$e$

$x$

$η$

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