Newton's Backward Difference Formula

$$f_p=f_0+p\nabla_0+{\textstyle{1\over 2!}}p(p+1)\nabla_0^2+{\textstyle{1\over 3!}}p(p+1)(p+2)\nabla_0^3+\ldots,$$

for $p\in[0,1]$, where $\nabla$ is the Backward Difference.

See also Newton's Forward Difference Formula

References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 433, 1987.