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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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MathML (17.471 KB / 2.406 KB) :

Γ μ ⁢ ν α := ∂ ⁡ x α ∂ ⁡ ξ ρ ⁢ ∂ 2 ⁡ ξ ρ ∂ ⁡ x μ ⁢ ∂ ⁡ x ν = 1 2 ⁢ g α ⁢ σ ⁢ ( g μ ⁢ σ , ν + g ν ⁢ σ , μ - g μ ⁢ ν , σ ) assign superscript subscript Γ 𝜇 𝜈 𝛼 superscript 𝑥 𝛼 superscript 𝜉 𝜌 superscript 2 superscript 𝜉 𝜌 superscript 𝑥 𝜇 superscript 𝑥 𝜈 1 2 superscript 𝑔 𝛼 𝜎 subscript 𝑔 𝜇 𝜎 𝜈 subscript 𝑔 𝜈 𝜎 𝜇 subscript 𝑔 𝜇 𝜈 𝜎 {\displaystyle{\displaystyle\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:=∂xα∂ξρ∂2ξρ∂xμ∂xν=12gασ(gμσ,ν+gνσ,μ−gμν,σ)

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