A sequence s_n^(λ)(x) = [h(t)]^λ s_n(x), where s_n(x) is a Sheffer sequence, h(t) is invertible, and λ ranges over the real numbers is called a Steffensen sequence. If s_n(x) is an associated Sheffer sequence, then s_n^(λ) is called a cross sequence. If s_n(x) = x^n, then s_n^(λ)(x) = [h(t)]^λ x^n is called an Appell cross sequence. Examples include the Bernoulli polynomial, Euler polynomial, and Hermite polynomial.

Appell sequence | cross sequence | Sheffer sequence | Steffensen sequence

Paul Emile Appell