The central difference for a function tabulated at equal intervals f_n is defined by δ(f_n) = δ_n = δ_n^1 = f_(n + 1/2) - f_(n - 1/2). First and higher order central differences arranged so as to involve integer indices are then given by δ_(n + 1/2) | = | δ_(n + 1/2)^1 | = | f_(n + 1) - f_n δ_n^2 | = | δ_(n + 1/2)^1 - δ_(n - 1/2)^1 | = | f_(n + 1) - 2f_n + f_(n - 1) δ_(n + 1/2)^3 | = | δ_(n + 1)^2 - δ_n^2 | = | f_(n + 2) - 3f_(n + 1) + 3f_n - f_(n - 1) (Abramowitz and Stegun 1972, p. 877).

backward difference | divided difference | forward difference