The classical umbral calculus and the flow of a Drinfeld module
The notion of a flow appears in many areas of mathematics and physics; for example, it is one of the fundamental notions in studying ordinary differential equations. Classically a flow on a set X is a group action of the additive group of the set of real numbers R on the set X One of the classical theorems in analysis, the classical Taylor theorem, can be expressed in terms of a flow. More precisely, let d/dt be the formal derivative acting on the polynomial ring R[t] For each x R, let e R[t] R[t] be the linear operator defined by