Delta Operator

A shift-invariant operator Q for which Qx is a nonzero constant.

1. Qa=0 for every constant a.

2. If p(x) is a polynomial of degree n, Qp(x) is a polynomial of degree n-1.

3. Every delta sequence has a unique basic polynomial sequence.

See also

Basic Polynomial Sequence, Shift-Invariant Operator, Umbral Calculus

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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.

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Delta Operator

Cite this as:

Weisstein, Eric W. "Delta Operator." From MathWorld--A Wolfram Web Resource.

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