Dictionary:Newtonian interpolation

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For a function known at regularly spaced points, yn=f(xo+nh), the value at yu=f(xo+uh) can be approximated by a series for which the kth term is u(u–1)...(ukkyo/k!, where Δ is the forward difference operator. A similar relationship can be used for backward prediction, its kth term being u(u+1)...(u+kkyo/k!.