WE have:

<br />
R_{\mu \nu}=R_{\mu \nu \lambda}^{\lambda}=\dfrac{\partial \Gamma_{\mu \lambda}^{\lambda}}{\partial x^{\nu}}-\dfrac{\partial \Gamma_{\mu \nu}^{\lambda}}{\partial x^{\lambda}}+\Gamma_{\mu \lambda}^{\beta} \Gamma_{\nu \beta}^{\lambda}-\Gamma_{\mu \nu}^{\beta} \Gamma_{\beta \lambda}^{\lambda}<br />

What's the purpouse of \lambda and \beta? What values can they take?