Backward Difference

The backward difference is a finite difference defined by

(1)

Higher order differences are obtained by repeated operations of the backward difference operator, so

			(2)
			(3)
			(4)

In general,

(5)

where  is a binomial coefficient.

The backward finite difference are implemented in the Wolfram Language as DifferenceDelta[f, i].

Newton's backward difference formula expresses  as the sum of the th backward differences

(6)

where  is the first th difference computed from the difference table.

REFERENCES:

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 429 and 433, 1987.