divergence in Einstein Summation

Question

I've learned that divergence of f in Cartesian coordinates is expressed as $\partial_if_i$ in Einstein Notation.

How would divergence in curvilinear coordinates be expressed in Einstein Notation?

$$\nabla\cdot \vec{v} = \frac{1}{h_1h_2h_3}[ \frac{\partial (v_1h_2h_3)}{\partial u_1} + \frac{\partial (h_1v_2h_3)}{\partial u_2} + \frac{\partial (h_1h_2v_3)}{\partial u_3}]. $$

Answer 1

I would suggest

$$\frac{1}{h_1 h_2 h_3} \partial_i \bigg( v_i \prod_{j \neq i} h_j \bigg)$$