Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Part of: Synthesis digital library of engineering and computer science.

Includes bibliographical references (page 91) and index.

1. Types of generating functions -- 1.1. Introduction -- 1.2. Notations and nomenclatures -- 1.3. Types of generating functions -- 1.4. Ordinary generating functions -- 1.5. Exponential generating functions (EGF) -- 1.6. Pochhammer generating functions -- 1.7. Other generating functions -- 1.8. Summary

2. Operations on generating functions -- 2.1. Basic operations -- 2.2. Invertible sequences -- 2.3. Composition of generating functions -- 2.4. Summary

3. Generating functions in statistics -- 3.1. Generating functions in statistics -- 3.2. Probability generating functions (PGF) -- 3.3. Generating functions for CDF -- 3.4. Generating functions for survival functions -- 3.5. Generating functions for mean deviation -- 3.6. MD of some distributions -- 3.7. Moment generating functions (MGF) -- 3.8. Characteristic functions -- 3.9. Cumulant generating functions -- 3.10. Factorial moment generating functions -- 3.11. Conditional moment generating functions (CMGF) -- 3.12. Generating functions of truncated distributions -- 3.13. Convergence of generating functions -- 3.14. Summary

4. Applications of generating functions -- 4.1. Applications in algebra -- 4.2. Applications in computing -- 4.3. Applications in combinatorics -- 4.4. Applications in graph theory -- 4.5. Applications in chemistry -- 4.6. Applications in epidemiology -- 4.7. Applications in number theory -- 4.8. Applications in statistics -- 4.9. Generating functions in reliability -- 4.10. Applications in bioinformatics -- 4.11. Applications in genetics -- 4.12. Applications in management -- 4.13. Applications in economics -- 4.14. Summary.

Abstract freely available; full-text restricted to subscribers or individual document purchasers.

Compendex

INSPEC

Google scholar

Google book search

This is an introductory book on generating functions (GFs) and their applications. It discusses commonly encountered generating functions in engineering and applied sciences, such as ordinary generating functions (OGF), exponential generating functions (EGF), probability generating functions (PGF), etc. Some new GFs like Pochhammer generating functions for both rising and falling factorials are introduced in Chapter 2. Two novel GFs called "mean deviation generating function" (MDGF) and "survival function generating function" (SFGF), are introduced in Chapter 3. The mean deviation of a variety of discrete distributions are derived using the MDGF. The last chapter discusses a large number of applications in various disciplines including algebra, analysis of algorithms, polymer chemistry, combinatorics, graph theory, number theory, reliability, epidemiology, bio-informatics, genetics, management, economics, and statistics. Some background knowledge on GFs is often assumed for courses in analysis of algorithms, advanced data structures, digital signal processing (DSP), graph theory, etc. These are usually provided by either a course on "discrete mathematics" or "introduction to combinatorics." But, GFs are also used in automata theory, bio-informatics, differential equations, DSP, number theory, physical chemistry, reliability engineering, stochastic processes, and so on. Students of these courses may not have exposure to discrete mathematics or combinatorics. This book is written in such a way that even those who do not have prior knowledge can easily follow through the chapters, and apply the lessons learned in their respective disciplines. The purpose is to give a broad exposure to commonly used techniques of combinatorial mathematics, highlighting applications in a variety of disciplines.

Also available in print.

Title from PDF title page (viewed on September 27, 2019).