What is the significance of the Δn difference operator in mathematics?

[Vodkacannon]

We all know the greek letter delta is the mathematical symbol that represents "change in."

I though about a new form of delta: Δⁿ. Where n² = the # of terms when you expand the delta operator.

For example: the usual Δx = x₂ - x₁
But now: Δ²x = (X₄-X₃) - (X₂-X₁). We can see that for Δ² there are 2² (4) terms.

Why the heck haven't I head of this notation. Does it just not exist? It does not seem to be used that much in mathematics.

Taking a Δⁿ is like taking the n^th derivative of a function is it not?

Wow. I discovered something by myself and I didn't even know it existed.
Look here: http://en.wikipedia.org/wiki/Difference_operator
Scroll down until you get to the title called "n^th difference"

 

[micromass]

In my understanding, it is mainly engineers (or at least: applied people) who work with finite difference methods. So if you don't care for applications, then it makes sense that you never heard of it.

Please correct me if I'm wrong.

 

[Stephen Tashi]

Wow. I discovered something by myself and I didn't even know it existed.
Look here: http://en.wikipedia.org/wiki/Difference_operator
Scroll down until you get to the title called "n^th difference"

The basic topic to look up is "The Calculus Of Finite Differences". A interesting book on the subject was written by George Boole himself.

 

[pwsnafu]

If you want to see how continuum calculus and finite calculus are related see time scales calculus.