ABSTRACT
In this chapter, the author recalls the definitions and properties of the mathematical infrastructure needed to accommodate generating functions. Power series can be introduced in a number of ways; it is probably appropriate to consider them as the basis for expansion of arbitrary functions, via the mechanism of Taylor series. There are three equivalent definitions of this concept; they are due to Riemann, Weierstrass, and Cauchy, respectively. They consider the set of continuous functions that have an arbitrary number of derivatives. Integration according to Riemann is not the only one possible—there are known many of its generalizations. They present the definition and properties of Stieltjes integral, which may lead to some notational and conceptual simplifications.
