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.
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arcsin 2
