Is the summation notation for three equivalent expressions?

[schwarzschild]

Are the following three equivalent?

$$P_{\alpha}A^{\beta}\tilde{\omega}^{\beta}(\vec{e_{\beta}} )$$ $$= \sum_{\alpha = 0}^{3}{P_{\alpha}\tilde{\omega}^{\alpha}(\sum_{\beta = 0}^{3}{A^{\beta}\vec{e}_{\beta}) = \sum_{\alpha = 0}^{3}{P_{\alpha}A^{\alpha}$$

 

[Fredrik]

The second equality is correct, assuming that the omegas are dual basis vectors. The first expression doesn't make sense, but it looks like a typo. Change the second beta to an alpha, and the first equality is good too.

 

[George Jones]

Don't use two sets of tex /tex tags; enclose the whole equality in one set of tex /tex tags.