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Display information for equation id:math.2547.65 on revision:2547

* Page found: Das ideale Fermigas (eq math.2547.65)

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Hash: 1defccfe1e4a76fffc26d35914eca4b9

TeX (original user input): 

\begin{align}

& U=\frac{\left( 2s+1 \right)}{2}\left( \frac{V}{{{h}^{3}}} \right)4\pi {{\left( 2mkT \right)}^{\frac{3}{2}}}kT\int_{0}^{\infty }{{}}dy\frac{{{y}^{\frac{3}{2}}}}{\left( {{e}^{y-\eta }}+1 \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}&U={\frac {\left(2s+1\right)}{2}}\left({\frac {V}{{h}^{3}}}\right)4\pi {{\left(2mkT\right)}^{\frac {3}{2}}}kT\int _{0}^{\infty }{}dy{\frac {{y}^{\frac {3}{2}}}{\left({{e}^{y-\eta }}+1\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}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (30.064 KB / 3.483 KB) :

U = ( 2 ⁢ s + 1 ) 2 ⁢ ( V h 3 ) ⁢ 4 ⁢ π ⁢ ( 2 ⁢ m ⁢ k ⁢ T ) 3 2 ⁢ k ⁢ T ⁢ ∫ 0 ∞ 𝑑 y ⁢ y 3 2 ( e y - η + 1 ) F 3 2 ⁢ ( η ) ≈ 4 3 ⁢ π ⁢ [ ( η ) 5 2 5 2 + π 2 4 ⁢ ( η ) 1 2 ] absent 𝑈 2 𝑠 1 2 𝑉 superscript ℎ 3 4 𝜋 superscript 2 𝑚 𝑘 𝑇 3 2 𝑘 𝑇 superscript subscript 0 differential-d 𝑦 superscript 𝑦 3 2 superscript 𝑒 𝑦 𝜂 1 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 U=\frac{\left(2% s+1\right)}{2}\left(\frac{V}{{{h}^{3}}}\right)4\pi{{\left(2mkT\right)}^{\frac{% 3}{2}}}kT\int_{0}^{\infty}{{}}dy\frac{{{y}^{\frac{3}{2}}}}{\left({{e}^{y-\eta}% }+1\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 (4.113 KB / 604 B) :

U=(2s+1)2(Vh3)4π(2mkT)32kT∫0∞dyy32(ey−η+1)F32(η)≈43π[(η)5252+π24(η)12]

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