How to interpret a Summation and Cartesian product together in a formula

[TheMarksman]

Hi all,

$$\sum_{i=1}^n k_i \Pi_{i=1}^n O_i(\mu)$$

How to interpret this equation.

 

[HallsofIvy]

Actually the way it is written makes it ambiguous. The index should not be "i" in both. My best guess is that better notation would be
$$\sum_{i=1}^n k_i \Pi_{j=1}^n O_j(\mu)$$
in which case we could take the product outside the sum so it would be just
$$\left(\sum_{i=1}^n k_i\right)\left(\Pi_{j=1}^n O_j(\mu)\right)$$
and now, since the sum and product are separated, we could write that as
$$\left(\sum_{i=1}^n k_i\right)\left(\Pi_{i=1}^n O_i(\mu)\right)$$

Perhaps that is what is meant.

 

[TheMarksman]

Thank you so much HallsofIvy.