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 Series expansion. 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.

**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.

© 1996-9

1999-05-25