有限差分
任意の正整数 k, n に対して Δ k h n ( f , x ) = ∑ i 1 = 0 k − 1 ∑ i 2 = 0 k − 1 ⋯ ∑ i n = 0 k − 1 Δ h n ( f , x + i 1 h + i 2 h + ⋯ + i n h ) . {\displaystyle \Delta _{kh}^{n}(f,x)=\sum \limits _{i_{1}=0}^{k-1}\sum \limits _{i_{2}=0}^{k-1}\cdots \sum \limits _{i_{n}=0}^{k-1}\Delta _{h}^{n}(f,x+i_{1}h+i_{2}h+\cdots +i_{n}h).}
ライプニッツ則: Δ h n ( f g , x ) = ∑ k = 0 n ( n k ) Δ h k ( f , x ) Δ h n − k ( g , x + k h ) . {\displaystyle \Delta _{h}^{n}(fg,x)=\sum \limits _{k=0}^{n}{\binom {n}{k}}\Delta _{h}^{k}(f,x)\Delta _{h}^{n-k}(g,x+kh).}