多項定理
( ∵ ( n ⋯ , − 1 , ⋯ ) = 0 ) {\displaystyle \left(\because {\binom {n}{\cdots ,-1,\cdots }}=0\right)}
= ∑ k 1 + ⋯ + k m = n + 1 [ ( n k 1 − 1 , k 2 , ⋯ , k m ) + ⋯ + ( n k 1 , ⋯ , k m − 1 , k m − 1 ) ] x 1 k 1 ⋯ x m k m {\displaystyle =\textstyle \sum \limits _{k_{1}+\cdots +k_{m}=n+1}\left[{\dbinom {n}{k_{1}-1,k_{2},\cdots ,k_{m}}}+\cdots +{\dbinom {n}{k_{1},\cdots ,k_{m-1},k_{m}-1}}\right]{x_{1}}^{k_{1}}\cdots {x_{m}}^{k_{m}}}