# Binomial coefficient

The binomial coefficient ${n \choose k}$ are defined for non-negative $n$ and $k$ by the formula $${n \choose k} = \dfrac{n!}{(n-k)!k!},$$ where $n!$ denotes the factorial. More generally, if $\alpha \in \mathbb{C}$ we define the (generalized) binomial coefficient by $${\alpha \choose k} = \dfrac{\alpha^{\underline{k}}}{k!},$$ where $\alpha^{\underline{k}}$ denotes the falling factorial.