A generating function is an algebraic function that represents a given sequence and the corresponding power series. Generating functions play a vital role in the area of enumerative combinatorics as an effective tool for determining different counting techniques. This book provides a comprehensive overview of different types of generating functions.

The book comprises four chapters. The first chapter is about the origin, existence, and nomenclature of generating functions. The chapter provides a detailed description of different types of generating functions, such as ordinary, exponential, Pochhammer, and so on, and their use in various fields such as number theory and combinatorics. The second chapter discusses the basic operations of generating functions: addition, products, powers, convolution, shifting, differentiation, and integration.

Chapter 3 describes some interesting generating functions in statistics. The discussion commences with probability generating functions, where the coefficients are the probabilities associated with a random variable and their properties. The authors then explain the probability generating functions corresponding to different probability distributions. The second half of the chapter describes generating functions for the cumulative distribution function (CDF), mean deviation, and moments, examining their properties in detail. The chapter ends with some other interesting functions, including characteristic functions, cumulant generating functions, factorial moment generating functions, and so on.

The fourth chapter discusses applying generating functions across disciplines. In addition to applications in mathematical fields such as algebra, computing, number theory, combinatorics, and graph theory, the authors present various applications in chemistry, biology, epidemiology, statistics, stochastic process, reliability theory, and management.

The content of the book is presented in a logical and interesting manner. It is a good fundamental reference book for students or researchers of algebraic combinatorics.