Newton's forward difference formula is a finite difference identity giving an interpolated value between tabulated points
in terms of the first value and the powers of the forward
difference . For , the formula states
(1)
When written in the form
(2)
with
the falling factorial, the formula looks suspiciously
like a finite analog of a Taylor series expansion.
This correspondence was one of the motivating forces for the development of umbral
calculus.
An alternate form of this equation using binomial coefficients is