---
title: Generating Functions
description: Generating functions encode numerical sequences as coefficients of formal power series. Learners will understand how to use algebraic operations on these series to solve recurrence relations and analyze complex combinatorial structures.
category: mathematics
subcategory: combinatorics
difficulty: beginner, intermediate, advanced
url: /subject/generating-functions
---

# Generating Functions

Generating functions encode numerical sequences as coefficients of formal power series. Learners will understand how to use algebraic operations on these series to solve recurrence relations and analyze complex combinatorial structures.

## Available Resources

2 Books • 1 Courses • 2 Websites

## Websites

### 1. Analytic Combinatorics

Official booksite for Flajolet and Sedgewick's Analytic Combinatorics, offering the full text as a free PDF, studio-recorded lecture videos with slides, and selected exercises. Covers symbolic methods, ordinary and exponential generating functions, singularity analysis and saddle-point asymptotics for counting combinatorial structures.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://ac.cs.princeton.edu/

**Tags:** analytic combinatorics, generating functions, asymptotic analysis, singularity analysis, enumerative combinatorics

### 2. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

## Books

### 1. Analytic Combinatorics

**Author:** Philippe Flajolet, Robert Sedgewick

Explore generating functions & combinatorial structures with "Analytic Combinatorics" by Flajolet & Sedgewick. Master advanced counting techniques!

**Difficulty:** Beginner | **Price:** Paid

**Link:** https://www.amazon.com/dp/0521898064?tag=edmonddante07-20

**Tags:** analytic combinatorics, generating functions, asymptotic analysis, singularity analysis, enumerative combinatorics

### 2. Generatingfunctionology

**Author:** Herbert S. Wilf

Learn generating functions! Explore combinatorial problem-solving with Herbert Wilf's classic "Generatingfunctionology."

**Difficulty:** Beginner | **Price:** Paid

**Link:** https://www.amazon.com/dp/1483248577?tag=edmonddante07-20

**Tags:** generating functions, enumerative combinatorics, power series, recurrence relations, combinatorial identities

## Courses

### 1. Combinatorial Mathematics

Discover how to apply counting principles and combinatorics to solve problems in computer science, financial analysis, and your daily life. This course focuses on introducing the concepts and ideas of combinatorial mathematics, and studies the counting methods and related theories of discrete objects.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://www.edx.org/learn/math/tsinghua-university-combinatorial-mathematics-zu-he-shu-xue

**Tags:** courses, mathematics-statistics, combinatorics

---

*This content is part of Dantes.io - Your Treasure Map to Knowledge*

*Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).*

View this page online: https://dantes.io/subject/generating-functions