- testwiki

General

Display information for equation id:math.1109.184 on revision:1109

* Page found: ART-Skript (eq math.1109.184)

Occurrences on the following pages:

Hash: 9850b80ee50de32dde46a35ce6211233

TeX (original user input):

\begin{align}
  & \Gamma '_{\nu \lambda }^{\mu }=\frac{\partial x{{'}^{\mu }}}{\partial {{\xi }^{\tau }}}\frac{{{\partial }^{2}}{{\xi }^{\tau }}}{\partial x{{'}^{\nu }}\partial x{{'}^{\lambda }}} \\ 
 & =\frac{\partial x{{'}^{\mu }}}{\partial {{\xi }^{\sigma }}}\frac{\partial {{x}^{\sigma }}}{\partial {{\xi }^{\tau }}}\frac{\partial }{\partial x{{'}^{\nu }}}\left( \frac{\partial {{\xi }^{\tau }}}{\partial {{x}^{\alpha }}}\frac{\partial {{x}^{\alpha }}}{\partial x{{'}^{\lambda }}} \right) \\ 
 & =\frac{\partial x{{'}^{\mu }}}{\partial {{\xi }^{\sigma }}}\frac{\partial {{x}^{\sigma }}}{\partial {{\xi }^{\tau }}}\left( \frac{{{\partial }^{2}}{{\xi }^{\tau }}}{\partial {{x}^{\alpha }}\partial {{x}^{\rho }}}\frac{\partial {{x}^{\rho }}}{\partial {{x}^{\alpha }}}\frac{\partial {{x}^{\alpha }}}{\partial x{{'}^{\lambda }}}+\frac{{{\partial }^{2}}{{x}^{\alpha }}}{\partial x{{'}^{\nu }}\partial x{{'}^{\lambda }}}\frac{\partial {{\xi }^{\tau }}}{\partial {{x}^{\alpha }}} \right) \\ 
 & =\frac{\partial x{{'}^{\mu }}}{\partial {{\xi }^{\sigma }}}\frac{\partial {{x}^{\sigma }}}{\partial {{\xi }^{\tau }}}\frac{\partial {{x}^{\alpha }}}{\partial x{{'}^{\lambda }}}\Gamma _{\alpha \rho }^{\sigma }+\frac{\partial x{{'}^{\mu }}}{\partial {{x}^{\sigma }}}\frac{{{\partial }^{2}}{{x}^{\sigma }}}{\partial x{{'}^{\nu }}\partial x{{'}^{\lambda }}}  
\end{align}

TeX (checked):

{\begin{aligned}&\Gamma '_{\nu \lambda }^{\mu }={\frac {\partial x{{'}^{\mu }}}{\partial {{\xi }^{\tau }}}}{\frac {{{\partial }^{2}}{{\xi }^{\tau }}}{\partial x{{'}^{\nu }}\partial x{{'}^{\lambda }}}}\\&={\frac {\partial x{{'}^{\mu }}}{\partial {{\xi }^{\sigma }}}}{\frac {\partial {{x}^{\sigma }}}{\partial {{\xi }^{\tau }}}}{\frac {\partial }{\partial x{{'}^{\nu }}}}\left({\frac {\partial {{\xi }^{\tau }}}{\partial {{x}^{\alpha }}}}{\frac {\partial {{x}^{\alpha }}}{\partial x{{'}^{\lambda }}}}\right)\\&={\frac {\partial x{{'}^{\mu }}}{\partial {{\xi }^{\sigma }}}}{\frac {\partial {{x}^{\sigma }}}{\partial {{\xi }^{\tau }}}}\left({\frac {{{\partial }^{2}}{{\xi }^{\tau }}}{\partial {{x}^{\alpha }}\partial {{x}^{\rho }}}}{\frac {\partial {{x}^{\rho }}}{\partial {{x}^{\alpha }}}}{\frac {\partial {{x}^{\alpha }}}{\partial x{{'}^{\lambda }}}}+{\frac {{{\partial }^{2}}{{x}^{\alpha }}}{\partial x{{'}^{\nu }}\partial x{{'}^{\lambda }}}}{\frac {\partial {{\xi }^{\tau }}}{\partial {{x}^{\alpha }}}}\right)\\&={\frac {\partial x{{'}^{\mu }}}{\partial {{\xi }^{\sigma }}}}{\frac {\partial {{x}^{\sigma }}}{\partial {{\xi }^{\tau }}}}{\frac {\partial {{x}^{\alpha }}}{\partial x{{'}^{\lambda }}}}\Gamma _{\alpha \rho }^{\sigma }+{\frac {\partial x{{'}^{\mu }}}{\partial {{x}^{\sigma }}}}{\frac {{{\partial }^{2}}{{x}^{\sigma }}}{\partial x{{'}^{\nu }}\partial x{{'}^{\lambda }}}}\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 (9.144 KB / 584 B) :

\begin{aligned} Γ'_{ν λ}^{μ} = \frac{\partial x'^{μ}}{\partial ξ^{τ}} \frac{\partial^{2} ξ^{τ}}{\partial x'^{ν} \partial x'^{λ}} \\ = \frac{\partial x'^{μ}}{\partial ξ^{σ}} \frac{\partial x^{σ}}{\partial ξ^{τ}} \frac{\partial}{\partial x'^{ν}} (\frac{\partial ξ^{τ}}{\partial x^{α}} \frac{\partial x^{α}}{\partial x'^{λ}}) \\ = \frac{\partial x'^{μ}}{\partial ξ^{σ}} \frac{\partial x^{σ}}{\partial ξ^{τ}} (\frac{\partial^{2} ξ^{τ}}{\partial x^{α} \partial x^{ρ}} \frac{\partial x^{ρ}}{\partial x^{α}} \frac{\partial x^{α}}{\partial x'^{λ}} + \frac{\partial^{2} x^{α}}{\partial x'^{ν} \partial x'^{λ}} \frac{\partial ξ^{τ}}{\partial x^{α}}) \\ = \frac{\partial x'^{μ}}{\partial ξ^{σ}} \frac{\partial x^{σ}}{\partial ξ^{τ}} \frac{\partial x^{α}}{\partial x'^{λ}} Γ_{α ρ}^{σ} + \frac{\partial x'^{μ}}{\partial x^{σ}} \frac{\partial^{2} x^{σ}}{\partial x'^{ν} \partial x'^{λ}} \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 mathvariant="normal">&#x0393;</mi><msubsup><mi>'</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x03BD;</mi><mi>&#x03BB;</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>&#x03BC;</mi></mrow></msubsup><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>&#x03BC;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>&#x03BE;</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C4;</mi></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>&#x2202;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>&#x03BE;</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C4;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>&#x03BD;</mi></mrow></msup><mi>&#x2202;</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>&#x03BB;</mi></mrow></msup></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>&#x03BC;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>&#x03BE;</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C3;</mi></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C3;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>&#x03BE;</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C4;</mi></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>&#x03BD;</mi></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>&#x03BE;</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C4;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>&#x03B1;</mi></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>&#x03B1;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>&#x03BB;</mi></mrow></msup></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>&#x03BC;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>&#x03BE;</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C3;</mi></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C3;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>&#x03BE;</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C4;</mi></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>&#x2202;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>&#x03BE;</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C4;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>&#x03B1;</mi></mrow></msup><mi>&#x2202;</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C1;</mi></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C1;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>&#x03B1;</mi></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>&#x03B1;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>&#x03BB;</mi></mrow></msup></mrow></mrow></mfrac></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>&#x2202;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>&#x03B1;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>&#x03BD;</mi></mrow></msup><mi>&#x2202;</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>&#x03BB;</mi></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>&#x03BE;</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C4;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>&#x03B1;</mi></mrow></msup></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>&#x03BC;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>&#x03BE;</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C3;</mi></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C3;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>&#x03BE;</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C4;</mi></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>&#x03B1;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>&#x03BB;</mi></mrow></msup></mrow></mrow></mfrac></mrow><msubsup><mi mathvariant="normal">&#x0393;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x03B1;</mi><mi>&#x03C1;</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>&#x03C3;</mi></mrow></msubsup><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>&#x03BC;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C3;</mi></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>&#x2202;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>&#x03C3;</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>&#x03BD;</mi></mrow></msup><mi>&#x2202;</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mi>&#x03BB;</mi></mrow></msup></mrow></mrow></mfrac></mrow></mtd></mtr></mtable></mrow></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$Γ$

$ν$

$λ$

$μ$

$x$

$μ$

$ξ$

$τ$

$ξ$

$τ$

$x$

$ν$

$x$

$λ$

$x$

$μ$

$ξ$

$σ$

$x$

$σ$

$ξ$

$τ$

$x$

$ν$

$ξ$

$τ$

$x$

$α$

$x$

$α$

$x$

$λ$

$x$

$μ$

$ξ$

$σ$

$x$

$σ$

$ξ$

$τ$

$ξ$

$τ$

$x$

$α$

$x$

$ρ$

$x$

$ρ$

$x$

$α$

$x$

$α$

$x$

$λ$

$x$

$α$

$x$

$ν$

$x$

$λ$

$ξ$

$τ$

$x$

$α$

$x$

$μ$

$ξ$

$σ$

$x$

$σ$

$ξ$

$τ$

$x$

$α$

$x$

$λ$

$Γ$

$α$

$ρ$

$σ$

$x$

$μ$

$x$

$σ$

$x$

$σ$

$x$

$ν$

$x$

$λ$

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