Appreciating Generating Functions as a Bridge between Discrete and Continuous Mathematics

Abstract

Generating functions transform an infinite sequence into the coefficients of a power series. It enables us to approach problem of sequence using the methods we have for algebraic problems. Given any power series, we treat this power series as an algebraic object where we have no concern in the convergence of the series. In this paper, we shall develop a generalized technique for constructing the generating functions of some algebraic functions, proper rational functions and binomial functions (both positive and negative powers) using method of differentiation. Also, we shall apply the techniques generalized in obtaining series expansion of some functions.