I am trying to understand the expression for Scalar curvature in terms of the Christoffel symbols.
This is given on Wikipedia by \begin{equation} S = g^{ab}(\Gamma^c_{ab,c} - \Gamma^c_{ac,b} + \Gamma^d_{ab}\Gamma^c_{cd} - \Gamma^d_{ac}\Gamma^c_{bd}) \end{equation} (see here for the Wikipedia post)
The thing I'm not sure about is the comma in expression $ab,c$, for example in the footer of the first Symbol. My guess would be that it means \begin{equation} \Gamma^c_{ab,c} = \partial_c \Gamma^c_{ab} \end{equation}
Is that correct ? The site on Christoffel Symbols on Wikipedia doesn't explain what the comma means so I was wondering whether somebody could help? Many thanks!