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.
