Welcome guest
You're not logged in.
278 users online, thereof 0 logged in

In analogy to the derivative $f’(x)=\lim_{h\to 0}\frac {f(x+h)-f(x)}{h},$ we introduce the difference operator as follows:

Definition: Difference Operator

Let \(D\subseteq\mathbb R\) (\(D\) is a subset of real numbers) and let \(f:D\to\mathbb R\) be a function. The difference operator $\Delta f$ is defined by $$\Delta f(x)=f(x-1)-f(x).$$


| | | | | created: 2020-03-23 20:57:53 | modified: 2020-03-23 21:13:45 | by: bookofproofs | references: [1112], [8404], [8405]

Edit or AddNotationAxiomatic Method

This work was contributed under CC BY-SA 4.0 by:

This work is a derivative of:

Bibliography (further reading)

[8405] Bool, George: “A Treatise on the Calculus of Finite Differences”, Dover Publications, Inc., 0

[1112] Graham L. Ronald, Knuth E. Donald, Patashnik Oren: “Concrete Mathematics”, Addison-Wesley, 1994, 2nd Edition

[8404] Miller, Kenneth S.: “An Introduction to the Calculus of Finite Differences And Difference Equations”, Dover Publications, Inc, 0