[ Γ a ] k l i = [ Γ b ] n p m ∂ [ x a ] i ∂ [ x b ] m ∂ [ x b ] n ∂ [ x a ] k ∂ [ x b ] p ∂ [ x a ] l + ∂ 2 [ x b ] m ∂ [ x a ] k ∂ [ x a ] l ∂ [ x a ] i ∂ [ x b ] m {\displaystyle \left[\Gamma _{a}\right]_{kl}^{i}=\left[\Gamma _{b}\right]_{np}^{m}{\frac {\partial \left[x_{a}\right]^{i}}{\partial \left[x_{b}\right]^{m}}}{\frac {\partial \left[x_{b}\right]^{n}}{\partial \left[x_{a}\right]^{k}}}{\frac {\partial \left[x_{b}\right]^{p}}{\partial \left[x_{a}\right]^{l}}}+{\frac {\partial ^{2}\left[x_{b}\right]^{m}}{\partial \left[x_{a}\right]^{k}\partial \left[x_{a}\right]^{l}}}{\frac {\partial \left[x_{a}\right]^{i}}{\partial \left[x_{b}\right]^{m}}}}
![{\displaystyle \left[\Gamma _{a}\right]_{kl}^{i}=\left[\Gamma _{b}\right]_{np}^{m}{\frac {\partial \left[x_{a}\right]^{i}}{\partial \left[x_{b}\right]^{m}}}{\frac {\partial \left[x_{b}\right]^{n}}{\partial \left[x_{a}\right]^{k}}}{\frac {\partial \left[x_{b}\right]^{p}}{\partial \left[x_{a}\right]^{l}}}+{\frac {\partial ^{2}\left[x_{b}\right]^{m}}{\partial \left[x_{a}\right]^{k}\partial \left[x_{a}\right]^{l}}}{\frac {\partial \left[x_{a}\right]^{i}}{\partial \left[x_{b}\right]^{m}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1ff13e265f220e47bc065b7b035d36eb41f3c50d)
