n-th Difference
The nth forward difference of a function f(x) is given by
where is the binomial coefficient. Forward differences applied to a sequence are sometimes called the binomial transform of the sequence, and have a number of interesting combinatorial properties.
Forward differences may be evaluated using the Nörlund–Rice integral. The integral representation for these types of series is interesting because the integral can often be evaluated using asymptotic expansion or saddle-point techniques; by contrast, the forward difference series can be extremely hard to evaluate numerically, because the binomial coefficients grow rapidly for large n.
Read more about this topic: Finite Difference
Famous quotes containing the word difference:
“The difference between human vision and the image perceived by the faceted eye of an insect may be compared with the difference between a half-tone block made with the very finest screen and the corresponding picture as represented by the very coarse screening used in common newspaper pictorial reproduction. The same comparison holds good between the way Gogol saw things and the way average readers and average writers see things.”
—Vladimir Nabokov (1899–1977)