- testwiki

General

Display information for equation id:math.2508.22 on revision:2508

* Page found: Reale Gase (eq math.2508.22)

Occurrences on the following pages:

Reale Gase Eq: math.2511.22

Hash: 6346c407c97d1dfbee12037f761d7f79

TeX (original user input):

\begin{align}

& Y=\sum\limits_{N=0}^{\infty }{{}}{{\xi }^{N}}{{Z}_{N}}=\sum\limits_{N=0}^{\infty }{{}}\frac{1}{N!}{{\left( \xi V \right)}^{N}}\left[ 1+N(N-1)\frac{B}{V} \right] \\

& \xi :=\rho \Phi \left( \beta  \right) \\

& Y=\sum\limits_{N=0}^{\infty }{{}}{{\xi }^{N}}{{Z}_{N}}=\sum\limits_{N=0}^{\infty }{{}}\frac{1}{N!}{{\left( \xi V \right)}^{N}}\left[ 1+N(N-1)\frac{B}{V} \right]=\exp \left( \xi V \right)+\frac{B}{V}{{\left( \xi V \right)}^{2}}\frac{{{\partial }^{2}}}{\partial {{\left( \xi V \right)}^{2}}}\exp \left( \xi V \right) \\

& =\exp \left( \xi V \right)\left( 1+{{\xi }^{2}}BV \right) \\

\end{align}

TeX (checked):

{\begin{aligned}&Y=\sum \limits _{N=0}^{\infty }{}{{\xi }^{N}}{{Z}_{N}}=\sum \limits _{N=0}^{\infty }{}{\frac {1}{N!}}{{\left(\xi V\right)}^{N}}\left[1+N(N-1){\frac {B}{V}}\right]\\&\xi :=\rho \Phi \left(\beta \right)\\&Y=\sum \limits _{N=0}^{\infty }{}{{\xi }^{N}}{{Z}_{N}}=\sum \limits _{N=0}^{\infty }{}{\frac {1}{N!}}{{\left(\xi V\right)}^{N}}\left[1+N(N-1){\frac {B}{V}}\right]=\exp \left(\xi V\right)+{\frac {B}{V}}{{\left(\xi V\right)}^{2}}{\frac {{\partial }^{2}}{\partial {{\left(\xi V\right)}^{2}}}}\exp \left(\xi V\right)\\&=\exp \left(\xi V\right)\left(1+{{\xi }^{2}}BV\right)\\\end{aligned}}

LaTeXML (experimental; uses MathML) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

MathML (experimental; no images) rendering

MathML (5.089 KB / 617 B) :

\begin{aligned} Y = \sum_{N = 0}^{\infty} ξ^{N} Z_{N} = \sum_{N = 0}^{\infty} \frac{1}{N!} {(ξ V)}^{N} [1 + N (N - 1) \frac{B}{V}] \\ ξ : = ρ Φ (β) \\ Y = \sum_{N = 0}^{\infty} ξ^{N} Z_{N} = \sum_{N = 0}^{\infty} \frac{1}{N!} {(ξ V)}^{N} [1 + N (N - 1) \frac{B}{V}] = \exp (ξ V) + \frac{B}{V} {(ξ V)}^{2} \frac{\partial^{2}}{\partial {(ξ V)}^{2}} \exp (ξ V) \\ = \exp (ξ V) (1 + ξ^{2} B V) \end{aligned}

<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi>Y</mi><mo>=</mo><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>N</mi><mo>=</mo><mn>0</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">&#x221E;</mi></mrow></munderover><msup><mi>&#x03BE;</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msup><msub><mi>Z</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo>=</mo><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>N</mi><mo>=</mo><mn>0</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">&#x221E;</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>N</mi><mi>!</mi></mrow></mrow></mfrac></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>&#x03BE;</mi><mi>V</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mn>1</mn><mo>+</mo><mi>N</mi><mo stretchy="false">(</mo><mi>N</mi><mo>&#x2212;</mo><mn>1</mn><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>B</mi></mrow><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>&#x03BE;</mi><mi>:</mi><mo>=</mo><mi>&#x03C1;</mi><mi mathvariant="normal">&#x03A6;</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>&#x03B2;</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>Y</mi><mo>=</mo><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>N</mi><mo>=</mo><mn>0</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">&#x221E;</mi></mrow></munderover><msup><mi>&#x03BE;</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msup><msub><mi>Z</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo>=</mo><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>N</mi><mo>=</mo><mn>0</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">&#x221E;</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>N</mi><mi>!</mi></mrow></mrow></mfrac></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>&#x03BE;</mi><mi>V</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mn>1</mn><mo>+</mo><mi>N</mi><mo stretchy="false">(</mo><mi>N</mi><mo>&#x2212;</mo><mn>1</mn><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>B</mi></mrow><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>=</mo><mi>exp</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>&#x03BE;</mi><mi>V</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>B</mi></mrow><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow></mfrac></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>&#x03BE;</mi><mi>V</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>&#x2202;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>&#x03BE;</mi><mi>V</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><mi>exp</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>&#x03BE;</mi><mi>V</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mi>exp</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>&#x03BE;</mi><mi>V</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo>+</mo><msup><mi>&#x03BE;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>B</mi><mi>V</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$Y$

$N$

$ξ$

$N$

$Z_{N}$

$N$

$N$

$ξ$

$V$

$N$

$N$

$N$

$B$

$V$

$ξ$

$ρ$

$Φ$

$β$

$Y$

$N$

$ξ$

$N$

$Z_{N}$

$N$

$N$

$ξ$

$V$

$N$

$N$

$N$

$B$

$V$

$ξ$

$V$

$B$

$V$

$ξ$

$V$

$ξ$

$V$

$ξ$

$V$

$ξ$

$V$

$ξ$

$B$

$V$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

General

LaTeXML (experimental; uses MathML) rendering

MathML (experimental; no images) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

General

LaTeXML (experimental; uses MathML) rendering

MathML (experimental; no images) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

Search