A shift-invariant operator 
for which 
is a nonzero constant.
1. 
for every constant 
.
2. If 
is a polynomial of degree 
, 
is a polynomial of degree 
.
3. Every delta sequence has a unique basic polynomial sequence.
Delta Operator
See also
Basic Polynomial Sequence, Shift-Invariant Operator, Umbral CalculusExplore with Wolfram|Alpha
References
Roman, S. The Umbral Calculus. New York: Academic Press, 1984.Rota, G.-C.; Kahaner, D.; Odlyzko, A. "On the Foundations of Combinatorial Theory. VIII: Finite Operator Calculus." J. Math. Anal. Appl. 42, 684-760, 1973.Referenced on Wolfram|Alpha
Delta OperatorCite this as:
Weisstein, Eric W. "Delta Operator." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DeltaOperator.html