An Introduction to Ordinary
Generating Functions

Mike Zabrocki
Mathematics and Statistics
York University

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                  just for decoration


This book is a short introduction to generating functions from a a computational perspective.  It is an experiment with new technology.

My goal is to cover only the topic of ordinary generating functions and only a quick introduction.  It does not extend beyond the computational aspects and does not cover more combinatorial applications of generating functions.  These are topics that I hope to cover in other short books.

Below I include the video summaries of the text which accompany each section.

Chapter 1: Introduction

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                  section 2.1 video
picture of Sage from section 1.2 video
Section 1.1: About this e-book
Section 1.2: Notes about recommended background of the reader

Chapter 2: Generating functions neither generate nor are they functions

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snapshot from section 2.2 video summary
Section 2.1: The three W's of generating functions (what, when why?)
Section 2.2: Examples

Chapter 3: Getting the most out of your generating functions

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snapshot from section 3.2 video summary
Section 3.1: Back and forth
Section 3.2: Examples

Chapter 4: Examples and exercises

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snapshot from section 4.2 video summary
Section 4.1: Exercises to help build strong generating functions
Section 4.2: Using generating functions to prove summation formulas

Section 4.3: Solutions

Chapter 5: Final words

After you have finished this book I hope that you have the basic tools to manipulate generating functions for sequences and that you are able to use them to prove basic identities.  This is a very good starting point, but you will find that what I have presented here only a very small part of the subject and you will need to find other references to learn more advanced aspects.

Date of original publication: September 25, 2013
Date of last update: September 25, 2013