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Date: 18-8-2021
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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) |
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(3) |
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(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.
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