Newton's Forward Difference Formula
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
When written in the form
with
the Pochhammer Symbol, the formula looks suspiciously like a finite analog of a Taylor Seriesexpansion. This correspondence was one of the motivating forces for the development of Umbral Calculus.The Derivative of Newton's forward difference formula gives Markoff's Formulas.
See also Finite Difference, Markoff's Formulas, Newton's Backward Difference Formula, Newton's DividedDifference Interpolation Formula
References
Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 880, 1972. Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 432, 1987.
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