Generating Functions in Engineering and the Applied Sciences

Contents
Tables
Glossary
Types of Generating Functions
	Introduction
	Notation & Nomenclature
		Rising & Falling Factorials
		Dummy Variable
	Types of Generating Functions
	Ordinary Generating Functions
		Recurrence Relations
		Types of Sequences
		OGF for Partial Sums
	Exponential Generating Functions (EGF)
	Pochhammer Generating Functions
		Rising Pochhammer GF (RPGF)
		Falling Pochhammer GF (FPGF)
	Other Generating Functions
		Auto-Covariance Generating Function
		Information Generating Function (IGF)
		Generating Functions in Graph Theory
		Generating Functions in Number Theory
		Rook Polynomial Generating Function
		Stirling Numbers of 2nd Kind
	Summary
Operations on Generating Functions
	Basic Operations
		Extracting Coefficients
		Addition & Subtraction
		Multiplication by Non-Zero Constant
		Linear Combination
		Shifting
		Functions of Dummy Variable
		Convolutions and Powers
		Differentiation & Integration
		Integration
	Invertible Sequences
	Composition of Generating Functions
	Summary
Generating Functions in Statistics
	Generating Functions in Statistics
	Probability Generating Functions (PGF)
	Generating Functions for CDF
	Generating Functions for Survival Functions
	Generating Functions for Mean Deviation
	MD of Some Distributions
		MD of Geometric Distribution
		MD of Binomial Distribution
		MD of Poisson distribution
		MD of Negative Binomial Distribution
	Moment Generating Functions (MGF)
	Characteristic Functions
	Cumulant Generating Functions
	Factorial Moment Generating Functions
	Conditional Moment Generating Functions (CMGF)
	Generating Functions of Truncated Distributions
	Convergence of Generating Functions
	Summary
Applications of Generating Functions
	Algebra
		Series involving Integer Parts
		Permutation Inversions
		Generating Function of Strided Sequences
	Computing
		Merge-Sort Algorithm Analysis
		Quick-Sort Algorithm Analysis
		Binary-Search Algorithm Analysis
		Well-formed Parentheses
		Formal Languages
	Combinatorics
		Combinatorial Identities
		New Generating Functions from old
		Recurrence Relations
		Towers of Hanoi Puzzle
	Graph Theory
		Graph Enumeration
		Tree Enumeration
	Chemistry
		Polymer Chemistry
		Counting Isomers of Hydrocarbons
	Epidemiology
	Number Theory
	Statistics
		Sums of IID Random Variables
		Infinite Divisibility
		Stochastic Processes
	Reliability
	Bioinformatics
	Genomics
	Management
	Economics
	Summary
Biblio
Index