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* Page found: Reale Gase (eq 17) (force rerendering)

Occurences on the following pages:

   Reale Gase Eq: 17
TeX (as stored in database):
\begin{align}
 
& {{Z}_{N}}=\frac{1}{N!}\Phi {{\left( \beta  \right)}^{N}}\left[ {{V}^{N}}+{{V}^{N-2}}\sum\limits_{i<j}^{{}}{{}}\int_{{}}^{{}}{{{d}^{3}}{{q}_{i}}}\int_{{}}^{{}}{{{d}^{3}}{{q}_{j}}}{{f}_{ij}}({{r}_{ij}})+..... \right] \\
 
& \int_{{}}^{{}}{{{d}^{3}}{{q}_{i}}}\int_{{}}^{{}}{{{d}^{3}}{{q}_{j}}}{{f}_{ij}}({{r}_{ij}})=\int_{V}^{{}}{{}}{{d}^{3}}q\int_{{}}^{{}}{{}}{{d}^{3}}rf(r) \\
 
& \Rightarrow {{Z}_{N}}=\frac{1}{N!}\Phi {{\left( \beta  \right)}^{N}}\left[ {{V}^{N}}+{{V}^{N-1}}\frac{N(N-1)}{2}\int_{{}}^{{}}{{}}{{d}^{3}}rf(r)+O\left( {{V}^{N-2}} \right) \right] \\
 
\end{align}
MathML (30.537 KB / 4.261 KB) :
ZN=1N!Φ(β)N[VN+VN-2i<jd3qid3qjfij(rij)+..]fragmentssubscriptZN1NΦsuperscriptfragmentsnormal-(βnormal-)Nfragmentsnormal-[superscriptVNsuperscriptVN2subscriptijsuperscriptd3subscriptqisuperscriptd3subscriptqjsubscriptfijfragmentsnormal-(subscriptrijnormal-)normal-…normal-.normal-.normal-]\displaystyle{{Z}_{{N}}}=\frac{1}{N!}\Phi{{\left(\beta\right)}^{{N}}}\left[{{V% }^{{N}}}+{{V}^{{N-2}}}\sum\limits_{{i<j}}{{}}\int{{{d}^{{3}}}{{q}_{{i}}}}\int{% {{d}^{{3}}}{{q}_{{j}}}}{{f}_{{ij}}}({{r}_{{ij}}})+.....\right]
d3qid3qjfij(rij)=Vd3qd3rf(r)superscriptd3subscriptqisuperscriptd3subscriptqjsubscriptfijsubscriptrijsubscriptVsuperscriptd3qsuperscriptd3rfr\displaystyle\int{{{d}^{{3}}}{{q}_{{i}}}}\int{{{d}^{{3}}}{{q}_{{j}}}}{{f}_{{ij% }}}({{r}_{{ij}}})=\int_{{V}}{{}}{{d}^{{3}}}q\int{{}}{{d}^{{3}}}rf(r)
ZN=1N!Φ(β)N[VN+VN-1N(N-1)2d3rf(r)+O(VN-2)]fragmentsnormal-⇒subscriptZN1NΦsuperscriptfragmentsnormal-(βnormal-)Nfragmentsnormal-[superscriptVNsuperscriptVN1NN12superscriptd3rffragmentsnormal-(rnormal-)Ofragmentsnormal-(superscriptVN2normal-)normal-]\displaystyle\Rightarrow{{Z}_{{N}}}=\frac{1}{N!}\Phi{{\left(\beta\right)}^{{N}% }}\left[{{V}^{{N}}}+{{V}^{{N-1}}}\frac{N(N-1)}{2}\int{{}}{{d}^{{3}}}rf(r)+O% \left({{V}^{{N-2}}}\right)\right]

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Hash : d8afac176fa7440f9e220edb36167262

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Variables

27 results

  • mi ! (2/13/276)
  • mo . (2/6/350)
  • mi O (1/7/754)
  • mi Z (2/20/945)
  • mi (1/6/989)
  • mo [ (2/5/1298)
  • mo ] (2/5/1300)
  • mi Φ (2/11/1376)
  • mo < (1/19/1435)
  • mi β (2/39/1458)
  • mo (1/22/1479)
  • mo (1/15/1888)
  • mo (7/29/2089)
  • mi V (6/211/3347)
  • mi f (4/22/3433)
  • mi j (7/28/3458)
  • mi q (5/16/5359)
  • mi d (7/65/6342)
  • mi N (13/85/6684)
  • mo + (4/54/6970)
  • mi i (7/38/7943)
  • mo - (4/106/10795)
  • mi r (6/86/14377)
  • mo = (3/144/18270)
  • mo ( (8/169/18822)
  • mo ) (8/169/18905)
  • mo (15/419/59187)

MathML


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xref="S0.Ex1.m2.1.cmml">\displaystyle{{Z}_{{N}}}=\frac{1}{N!}\Phi{{\left(\beta\right)}^{{N}}}\left[{{V%
}^{{N}}}+{{V}^{{N-2}}}\sum\limits_{{i&lt;j}}{{}}\int{{{d}^{{3}}}{{q}_{{i}}}}\int{%
{{d}^{{3}}}{{q}_{{j}}}}{{f}_{{ij}}}({{r}_{{ij}}})+.....\right]</annotation></semantics></math></td>
<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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}}}({{r}_{{ij}}})=\int_{{V}}{{}}{{d}^{{3}}}q\int{{}}{{d}^{{3}}}rf(r)</annotation></semantics></math></td>
<td class="eqpad"/></tr>
<tr id="S0.Ex3" class="equation baseline">
<td class="eqpad"/>
<td colspan="1" class="td right" style="text-align:right;"/>
<td colspan="1" class="td left" style="text-align:left;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\displaystyle\Rightarrow{{Z}_{{N}}}=\frac{1}{N!}\Phi{{\left(\beta\right)}^{{N}%&#10;}}\left[{{V}^{{N}}}+{{V}^{{N-1}}}\frac{N(N-1)}{2}\int{{}}{{d}^{{3}}}rf(r)+O%&#10;\left({{V}^{{N-2}}}\right)\right]" id="S0.Ex3.m2.1" display="inline" xref="S0.Ex3.m2.1.cmml"><semantics id="S0.Ex3.m2.1a" xref="S0.Ex3.m2.1.cmml"><mrow id="S0.Ex3.m2.1b" xref="S0.Ex3.m2.1.cmml"><mo id="S0.Ex3.m2.1.1" xref="S0.Ex3.m2.1.1.cmml"></mo><msub id="S0.Ex3.m2.1.33" xref="S0.Ex3.m2.1.33.cmml"><mi id="S0.Ex3.m2.1.2" xref="S0.Ex3.m2.1.2.cmml">Z</mi><mi id="S0.Ex3.m2.1.3.1" xref="S0.Ex3.m2.1.3.1.cmml">N</mi></msub><mo id="S0.Ex3.m2.1.4" xref="S0.Ex3.m2.1.4.cmml">=</mo><mstyle displaystyle="true" id="S0.Ex3.m2.1.5" xref="S0.Ex3.m2.1.5.cmml"><mfrac id="S0.Ex3.m2.1.5a" xref="S0.Ex3.m2.1.5.cmml"><mn id="S0.Ex3.m2.1.5.2" xref="S0.Ex3.m2.1.5.2.cmml">1</mn><mrow id="S0.Ex3.m2.1.5.3" xref="S0.Ex3.m2.1.5.3.cmml"><mi 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xref="S0.Ex3.m2.1.35.5"><csymbol cd="ambiguous" id="S0.Ex3.m2.1.35.5a.cmml" xref="S0.Ex3.m2.1.35.5">fragments</csymbol><ci id="S0.Ex3.m2.1.28.cmml" xref="S0.Ex3.m2.1.28">normal-(</ci><apply id="S0.Ex3.m2.1.35.5.1.cmml" xref="S0.Ex3.m2.1.35.5.1"><csymbol cd="ambiguous" id="S0.Ex3.m2.1.35.5.1.1.cmml">superscript</csymbol><ci id="S0.Ex3.m2.1.29.cmml" xref="S0.Ex3.m2.1.29">V</ci><apply id="S0.Ex3.m2.1.30.1.cmml" xref="S0.Ex3.m2.1.30.1"><minus id="S0.Ex3.m2.1.30.1.2.cmml" xref="S0.Ex3.m2.1.30.1.2"/><ci id="S0.Ex3.m2.1.30.1.1.cmml" xref="S0.Ex3.m2.1.30.1.1">N</ci><cn type="integer" id="S0.Ex3.m2.1.30.1.3.cmml" xref="S0.Ex3.m2.1.30.1.3">2</cn></apply></apply><ci id="S0.Ex3.m2.1.31.cmml" xref="S0.Ex3.m2.1.31">normal-)</ci></cerror><ci id="S0.Ex3.m2.1.32.cmml" xref="S0.Ex3.m2.1.32">normal-]</ci></cerror></cerror></annotation-xml><annotation id="S0.Ex3.m2.1c" encoding="application/x-tex" xref="S0.Ex3.m2.1.cmml">\displaystyle\Rightarrow{{Z}_{{N}}}=\frac{1}{N!}\Phi{{\left(\beta\right)}^{{N}%
}}\left[{{V}^{{N}}}+{{V}^{{N-1}}}\frac{N(N-1)}{2}\int{{}}{{d}^{{3}}}rf(r)+O%
\left({{V}^{{N-2}}}\right)\right]</annotation></semantics></math></td>
<td class="eqpad"/></tr>
</table>