A sequence

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

Examples include the actuarial polynomial and Poisson-Charlier polynomial.

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

CITE THIS AS:

Weisstein, Eric W. "Cross Sequence." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CrossSequence.html