An Appell sequence is a Sheffer sequence for (g(t), t). Roman summarizes properties of Appell sequences and gives a number of specific examples. The sequence s_n(x) is Appell for g(t) iff 1/(g(t)) e^(y(t)) = sum_(k = 0)^∞ (s_k(y))/(k!) t^k for all y in the field C of field characteristic 0, and iff s_n(x) = x^n/(g(t)) (Roman 1984, p. 27).

Appell cross sequence | Sheffer sequence | umbral calculus