A λ μ ; ν = ∂ A λ μ ∂ x ν + Γ ρ ν λ A ρ μ − Γ μ ν ρ A λ ρ {\displaystyle {A^{\color {Violet}\lambda }}_{{\color {Orange}\mu };{\color {Red}\nu }}={\frac {\partial {A^{\color {Violet}\lambda }}_{\color {Orange}\mu }}{\partial {x^{\color {Red}\nu }}}}+\Gamma _{\rho {\color {Red}\nu }}^{\color {Violet}\lambda }{A^{\rho }}_{\color {Orange}\mu }-\Gamma _{{\color {Orange}\mu }{\color {Red}\nu }}^{\rho }{A^{\color {Violet}\lambda }}_{\rho }}
