Delta n: Exploring the nth Difference Operator

[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.

 

[CellCoree]

Thank you for sharing your discovery! The Delta n operator, also known as the nth difference operator, is a valuable tool in mathematics for analyzing patterns and sequences. It is essentially the same as taking the nth derivative of a function, but with discrete values instead of continuous ones. This notation is not as commonly used as the traditional delta symbol, but it is a valid and useful concept in mathematics. I encourage you to continue exploring and utilizing this operator in your work.