Generalization of Binomial Coefficients to any non negative real number.

Question

How could we put a product of $n$ values, $x_{1},\, x_{2},\,\,\,\,\,....x_{n}$ into binomial coefficients. I mean $\prod\limits_{i=1}^{n}x_{i}=$ Some expression involving binomial coefficients. Note that all $x_{i}$ are non-negative real numbers and having the relation $x_{1}\geq x_{2}\geq x_{3}....\geq x_{n}$. Relation to Gamma function or factorial function will also be helpful. Thanks