Steffensen Sequence

A sequence

where  is a Sheffer sequence,  is invertible, and  ranges over the real numbers. If  is an associated Sheffer sequence, then  is called a cross sequence. If , then

is called an Appell cross sequence.

An example is the Laguerre polynomial.

REFERENCES:

Brown, J. W. and Goldberg, J. L. "A Note on Generalized Appell Polynomials." Amer. Math. Monthly 75, 169-170, 1968.

Roman, S. "Cross Sequences and Steffensen Sequences." §5.3 in The Umbral Calculus. New York: Academic Press, pp. 140-143, 1984.

Rota, G.-C.; Kahaner, D.; and Odlyzko, A. "On the Foundations of Combinatorial Theory VIII: Finite Operator Calculus." J. Math. Anal. Appl. 42, 684-760, 1973.