An operator 
which maps some basic polynomial sequence 
into another basic
polynomial sequence 
.
Umbral Operator
See also
Basic Polynomial SequenceExplore with Wolfram|Alpha
References
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
Umbral OperatorCite this as:
Weisstein, Eric W. "Umbral Operator." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/UmbralOperator.html