Calcul tensoriel/Notions élémentaires/Symbole de Christoffel/Changement de coordonnées

$\left[\Gamma_a\right]^i_{kl} = \left[\Gamma_b\right]^m_{np} \frac{\partial\left[x_a\right]^i}{\partial\left[x_b\right]^m} \frac{\partial\left[x_b\right]^n}{\partial\left[x_a\right]^p} \frac{\partial\left[x_b\right]^p}{\partial\left[x_a\right]^l} + \frac{\partial^2\left[x_b\right]^m}{\partial\left[x_a\right]^k\partial\left[x_a\right]^l} \frac{\partial\left[x_a\right]^i}{\partial\left[x_b\right]^m}$