difference operator

The forward difference is a finite difference defined by Δ a_n congruent a_(n + 1) - a_n. Higher order differences are obtained by repeated operations of the forward difference operator, Δ^k a_n = Δ^(k - 1) a_(n + 1) - Δ^(k - 1) a_n, so Δ^2 a_n | = | (Δ_n)^2 | = | Δ(Δ_n) | = | Δ(a_(n + 1) - a_n) | = | Δ_(n + 1) - Δ_n | = | a_(n + 2) - 2a_(n + 1) + a_n.

backward difference | central difference | divided difference | Newton's forward difference formula | reciprocal difference