# Semi-colon vs nabla notation

## Main Question or Discussion Point

Is it

$$\nabla_\mu\nabla_\nu A^\alpha={A^\alpha}_{;\mu\nu}$$

or

$$\nabla_\mu\nabla_\nu A^\alpha={A^\alpha}_{;\nu\mu}$$

?

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dextercioby
Homework Helper
The second is the right one.

$$\nabla_\mu \nabla_\nu A^\alpha=\left(A^{\alpha}_{~;\nu}\right)_{;\mu}= A^{\alpha}_{~;\nu;\mu} = A^{\alpha}_{~;\nu\mu}$$

To avoid errors, my suggestion is not to use them both at the same time when making calculations.

CompuChip