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Display information for equation id:math.1107.181 on revision:1107

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TeX (original user input):

\Gamma _{\mu \nu }^{\alpha }:=\frac{\partial {{x}^{\alpha }}}{\partial {{\xi }^{\rho }}}\frac{{{\partial }^{2}}{{\xi }^{\rho }}}{\partial {{x}^{\mu }}\partial {{x}^{\nu }}}=\frac{1}{2}{{g}^{\alpha \sigma }}\left( {{g}_{\mu \sigma ,\nu }}+{{g}_{\nu \sigma ,\mu }}-{{g}_{\mu \nu ,\sigma }} \right)

TeX (checked):

\Gamma _{\mu \nu }^{\alpha }:={\frac {\partial {{x}^{\alpha }}}{\partial {{\xi }^{\rho }}}}{\frac {{{\partial }^{2}}{{\xi }^{\rho }}}{\partial {{x}^{\mu }}\partial {{x}^{\nu }}}}={\frac {1}{2}}{{g}^{\alpha \sigma }}\left({{g}_{\mu \sigma ,\nu }}+{{g}_{\nu \sigma ,\mu }}-{{g}_{\mu \nu ,\sigma }}\right)

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Γμνα:=xαξρ2ξρxμxν=12gασ(gμσ,ν+gνσ,μgμν,σ)
<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msubsup><mi>Γ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>μ</mi><mi>ν</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msubsup><mo stretchy="false">:=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi></mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi></mi><msup><mi>ξ</mi><mrow data-mjx-texclass="ORD"><mi>ρ</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></mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>ξ</mi><mrow data-mjx-texclass="ORD"><mi>ρ</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi></mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mi></mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><msup><mi>g</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>α</mi><mi>σ</mi></mrow></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>g</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>μ</mi><mi>σ</mi><mo>,</mo><mi>ν</mi></mrow></mrow></msub><mo stretchy="false">+</mo><msub><mi>g</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>ν</mi><mi>σ</mi><mo>,</mo><mi>μ</mi></mrow></mrow></msub><mo stretchy="false"></mo><msub><mi>g</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>μ</mi><mi>ν</mi><mo>,</mo><mi>σ</mi></mrow></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mstyle></mrow></math>

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Identifiers

  • Γ
  • μ
  • ν
  • α
  • x
  • α
  • ξ
  • ρ
  • ξ
  • ρ
  • x
  • μ
  • x
  • ν
  • g
  • α
  • σ
  • gμσ,ν
  • gνσ,μ
  • gμν,σ

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