Zur Navigation springen Zur Suche springen

General

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

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

(force rerendering)

Occurrences on the following pages:

Hash: e1b79b88f7a5648ee0d7456290beb90f

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}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (31.197 KB / 3.435 KB) :

x = y - η ⇒ Γ ⁢ ( s + 1 ) ⁢ F s ⁢ ( η ) = 1 s + 1 ⁢ ∫ 0 ∞ 𝑑 y ⁢ y s + 1 ⁢ e y - η ( e y - η + 1 ) 2 = 1 s + 1 ⁢ ∫ - η ∞ 𝑑 x ⁢ ( x + η ) s + 1 ⁢ e x ( e x + 1 ) 2 η ≫ 1 absent 𝑥 𝑦 𝜂 absent ⇒ absent Γ 𝑠 1 subscript 𝐹 𝑠 𝜂 1 𝑠 1 superscript subscript 0 differential-d 𝑦 superscript 𝑦 𝑠 1 superscript 𝑒 𝑦 𝜂 superscript superscript 𝑒 𝑦 𝜂 1 2 1 𝑠 1 superscript subscript 𝜂 differential-d 𝑥 superscript 𝑥 𝜂 𝑠 1 superscript 𝑒 𝑥 superscript superscript 𝑒 𝑥 1 2 absent much-greater-than 𝜂 1 {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle x=y-\eta\\ \par&\displaystyle\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}}}\\ \par&\displaystyle\eta>>1\\ \par\end{aligned}}}

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimentell; keine Bilder) rendering

MathML (3.385 KB / 540 B) :

x=y−η⇒Γ(s+1)Fs(η)=1s+1∫0∞dyys+1ey−η(ey−η+1)2=1s+1∫−η∞dx(x+η)s+1ex(ex+1)2η>>1

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Das ideale Fermigas page

Identifiers

  • x
  • y
  • η
  • Γ
  • s
  • Fs
  • η
  • s
  • y
  • y
  • s
  • e
  • y
  • η
  • e
  • y
  • η
  • s
  • η
  • x
  • x
  • η
  • s
  • e
  • x
  • e
  • x
  • η

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Abgerufen von „https://wiki.physikerwelt.de/wiki/Spezial:Formelinformation“