Appell Cross Sequence

A sequence


where s_n(x) is a Sheffer sequence, h(t) is invertible, and lambda ranges over the real numbers is called a Steffensen sequence. If s_n(x) is an associated Sheffer sequence, then s_n^((lambda)) is called a cross sequence. If s_n(x)=x^n, then


is called an Appell cross sequence.

Examples include the Bernoulli polynomial, Euler polynomial, and Hermite polynomial.

See also

Appell Sequence, Cross Sequence, Sheffer Sequence, Steffensen Sequence

Explore with Wolfram|Alpha


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.

Referenced on Wolfram|Alpha

Appell Cross Sequence

Cite this as:

Weisstein, Eric W. "Appell Cross Sequence." From MathWorld--A Wolfram Web Resource.

Subject classifications