ABSTRACT
Chapter 2 was focused on generating functions. Beginning with the simplest of infinite series, we developed familiarity with the features of generating functions and became comfortable with the idea of shuttling back and forth between generating functions and infinite series whose sum they represent. While rewarding in itself, the long range goal all along has been to apply this new knowledge to the solution of difference equations. This chapter will concentrate on applying these new found skills to the classes of difference equations introduced in Chapter 1. At the conclusion of this chapter, the reader’s ability to solve generating functions of all orders, both homogeneous and nonhomogeneous difference equations should be quite advanced. As has been our habit, we will start with the application of generating functions to the simplest of difference equations, gradually increasing our ability as we move to more complex ones. Throughout our work, we will remain focused on the three steps of the application of generating functions to difference equations: conversion, condensation, and inversion. The reader should feel free to return to Chapters 2 and 3 to review necessary sections of the development of generating functions as our requirements of them increase.
