Forward Difference
المؤلف:
Abramowitz, M. and Stegun, I. A
المصدر:
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover
الجزء والصفحة:
...
28-11-2021
1376
Forward Difference
The forward difference is a finite difference defined by
 |
(1)
|
Higher order differences are obtained by repeated operations of the forward difference operator,
 |
(2)
|
so
In general,
 |
(8)
|
where 
is a binomial coefficient (Sloane and Plouffe 1995, p. 10).
The forward finite difference is implemented in the Wolfram Language as DifferenceDelta[f, i].
Newton's forward difference formula expresses 
as the sum of the 
th forward differences
 |
(9)
|
where 
is the first 
th difference computed from the difference table. Furthermore, if the differences 
, 
, 
, ..., are known for some fixed value of 
, then a formula for the 
th term is given by
 |
(10)
|
(Sloane and Plouffe 1985, p. 10).
REFERENCES:
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 877, 1972.
Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego, CA: Academic Press, p. 10, 1995.
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