◀ ▲ ▶Branches / Combinatorics / Definition: Indefinite Sum, Antidifference
In analogy to the indefinite integral being the inverse operator to the derivative, we now define a similar concept for the difference operator.
Definition: Indefinite Sum, Antidifference
For a given complexvalued function $F:\mathbb C\to\mathbb C$, let the function $f:\mathbb C\to\mathbb C$ be defined by the difference operator $$f(x):=\Delta F(x).$$
The indefinite sum is the operation $$\sum f(x):=\Delta^{1}f(x)=F(x).$$ Because of this property, the function $F$ is also called the antidifference of $f.$
Table of Contents
 Proposition: Antidifferences are Unique Up to a Periodic Constant
Mentioned in:
Chapters: 1
Proofs: 2 3 4
Propositions: 5 6
Theorems: 7
Thank you to the contributors under CC BYSA 4.0!
 Github:

References
Bibliography
 Graham L. Ronald, Knuth E. Donald, Patashnik Oren: "Concrete Mathematics", AddisonWesley, 1994, 2nd Edition
 Miller, Kenneth S.: "An Introduction to the Calculus of Finite Differences And Difference Equations", Dover Publications, Inc, 1960
 Bool, George: "A Treatise on the Calculus of Finite Differences", Dover Publications, Inc., 1960