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* Page found: Reale Gase (eq 10) (force rerendering)

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   Reale Gase Eq: 10
TeX (as stored in database):
\begin{align}
 
& \frac{1}{N!}\Phi {{\left( \beta  \right)}^{N}}\int_{V}^{{}}{{}}{{d}^{3}}{{q}_{1}}...\int_{V}^{{}}{{}}{{d}^{3}}{{q}_{N}}\prod\limits_{i<j}^{{}}{{}}\left( 1+{{f}_{ij}} \right) \\
 
& \approx \frac{1}{N!}\Phi {{\left( \beta  \right)}^{N}}\int_{V}^{{}}{{}}{{d}^{3}}{{q}_{1}}...\int_{V}^{{}}{{}}{{d}^{3}}{{q}_{N}}\left( 1+\sum\limits_{i<j}^{{}}{{}}{{f}_{ij}}+\sum\limits_{\begin{smallmatrix}
 
i<j \\
 
k<l
 
\end{smallmatrix}}^{{}}{{}}{{f}_{ij}}{{f}_{kl}}+.... \right) \\
 
\end{align}
MathML (21.551 KB / 3.215 KB) :
1N!Φ(β)NVd3q1Vd3qNi<j(1+fij)1Nnormal-ΦsuperscriptβNsubscriptVsuperscriptd3subscriptq1normal-…subscriptVsuperscriptd3subscriptqNsubscriptproductij1subscriptfij\displaystyle\frac{1}{N!}\Phi{{\left(\beta\right)}^{{N}}}\int_{{V}}{{}}{{d}^{{% 3}}}{{q}_{{1}}}...\int_{{V}}{{}}{{d}^{{3}}}{{q}_{{N}}}\prod\limits_{{i<j}}{{}}% \left(1+{{f}_{{ij}}}\right)
1N!Φ(β)NVd3q1Vd3qN(1+i<jfij+i<jk<lfijfkl+.)fragments1NΦsuperscriptfragmentsnormal-(βnormal-)NsubscriptVsuperscriptd3subscriptq1normal-…subscriptVsuperscriptd3subscriptqNfragmentsnormal-(1subscriptijsubscriptfijsubscript<ij<klsubscriptfijsubscriptfklnormal-…normal-.normal-)\displaystyle\approx\frac{1}{N!}\Phi{{\left(\beta\right)}^{{N}}}\int_{{V}}{{}}% {{d}^{{3}}}{{q}_{{1}}}...\int_{{V}}{{}}{{d}^{{3}}}{{q}_{{N}}}\left(1+\sum% \limits_{{i<j}}{{}}{{f}_{{ij}}}+\sum\limits_{{\begin{smallmatrix}\par i<j\\ \par k<l\par \end{smallmatrix}}}{{}}{{f}_{{ij}}}{{f}_{{kl}}}+....\right)

SVG (0 B / 8 B) :
PNG (0 B / 8 B) :
Hash : ec03fed2cecfbf54f3b2f6c000c66f4f

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Variables

23 results

  • mo (1/1/38)
  • mi ! (2/13/276)
  • mo . (1/6/350)
  • mo (1/9/456)
  • mi (3/6/989)
  • mi Φ (2/11/1376)
  • mo < (4/19/1435)
  • mi β (2/39/1458)
  • mo (2/15/1888)
  • mo (4/29/2089)
  • mi V (4/211/3347)
  • mi f (4/22/3433)
  • mi j (6/28/3458)
  • mi l (2/3/4814)
  • mi q (4/16/5359)
  • mi k (2/21/6223)
  • mi d (4/65/6342)
  • mi N (6/85/6684)
  • mo + (4/54/6970)
  • mi i (6/38/7943)
  • mo ( (4/169/18822)
  • mo ) (4/169/18905)
  • mo (12/419/59187)

MathML


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cd="ambiguous" id="S0.Ex1.m2.1.30.3.2.4.2.4.2.1.1.cmml">subscript</csymbol><ci id="S0.Ex1.m2.1.27.cmml" xref="S0.Ex1.m2.1.27">f</ci><apply id="S0.Ex1.m2.1.28.1.cmml" xref="S0.Ex1.m2.1.28.1"><times id="S0.Ex1.m2.1.28.1.3.cmml" xref="S0.Ex1.m2.1.28.1.3"/><ci id="S0.Ex1.m2.1.28.1.1.cmml" xref="S0.Ex1.m2.1.28.1.1">i</ci><ci id="S0.Ex1.m2.1.28.1.2.cmml" xref="S0.Ex1.m2.1.28.1.2">j</ci></apply></apply></apply></apply></apply></apply></apply></apply></apply></annotation-xml><annotation id="S0.Ex1.m2.1b" encoding="application/x-tex" xref="S0.Ex1.m2.1.cmml">\displaystyle\frac{1}{N!}\Phi{{\left(\beta\right)}^{{N}}}\int_{{V}}{{}}{{d}^{{%
3}}}{{q}_{{1}}}...\int_{{V}}{{}}{{d}^{{3}}}{{q}_{{N}}}\prod\limits_{{i&lt;j}}{{}}%
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<td class="eqpad"/></tr>
<tr id="S0.Ex2" class="equation baseline">
<td class="eqpad"/>
<td colspan="1" class="td right" style="text-align:right;"/>
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{{d}^{{3}}}{{q}_{{1}}}...\int_{{V}}{{}}{{d}^{{3}}}{{q}_{{N}}}\left(1+\sum%
\limits_{{i&lt;j}}{{}}{{f}_{{ij}}}+\sum\limits_{{\begin{smallmatrix}\par
 i&lt;j\\
\par
 k&lt;l\par
\end{smallmatrix}}}{{}}{{f}_{{ij}}}{{f}_{{kl}}}+....\right)</annotation></semantics></math></td>
<td class="eqpad"/></tr>
</table>