Product of numbers (${\prod }_{i=1}^n{a}_i$)

The product of numbers $a_1,\dots ,a_n$ is the result of their iterated multiplication. The empty product is $1$, the multiplicative identity. For positive factors, $\log ({\prod }_i{a}_i)={\sum }_i\log a_i$, turning a multiplicative conservation law into an additive derivative identity.