does it have a name : $\prod\left(1-x_i\right)$

Question

I want to know whether there is a formula or theorem on the expansion of this expression: $$ \prod_{i=1}^n \left(1-x_i\right). $$ I only know the bionomial theorem and multinomiol theorem, but this one seems not those cases.

Thanks.

Answer 1

It is a special case of Vieta's formulas $\displaystyle\prod_{i=1}^n (z-x_i)=\sum_{k=0}^n(-1)^ke_k(x_1,\cdots,x_n)z^{n-k}$ with $z=1$.