tensor notation

Hi all,



Could someone explain, please, how the following expression can be written in component notation according to summation convention?



a^{kj};k + G^j_{km} a^{km} + G^k_{km} a^{mj}



it is the case of general tensors (non Cartesian)

indices k, j, m take values 1, 2, 3

G^j_{km} is Christoffel symbol of the second kind

; denotes partial differentiation (it is not covariant differentiation)



The first term is written a^{1j};1 + a^{2j};2 + a^{3j};3