Editing Umbral calculus (section)

== History ==
In the 1930s and 1940s, [[Eric Temple Bell]] attempted to set the umbral calculus on a rigorous footing, however his attempt in making this kind of argument logically rigorous was unsuccessful.

The [[combinatorics|combinatorialist]] [[John Riordan (mathematician)|John Riordan]] in his book ''Combinatorial Identities'' published in the 1960s, used techniques of this sort extensively.

In the 1970s, [[Steven Roman]], [[Gian-Carlo Rota]], and others developed the umbral calculus by means of [[linear functional]]s on spaces of polynomials. Currently, ''umbral calculus'' refers to the study of [[Sheffer sequence]]s, including polynomial sequences of [[binomial type]] and [[Appell sequence]]s, but may encompass systematic correspondence techniques of the [[calculus of finite differences]].