This book provides an introductory overview of generating functions (GFs) and their applications. The authors begin by providing background information on the origin of GFs. The book then introduces the most commonly encountered GFs in engineering and applied sciences, such as ordinary GFs, exponential GFs, and probability GFs. This third edition includes an expanded discussion of the applications of GFs in a variety of applied science and engineering fields. The authors have also added two new chapters that cover the applications in mathematics and computer science, including algebra, combinatorics, geometry, graph theory, number theory, trigonometry, algorithm analysis, signal processing, and machine learning.

Provides readers with an essential overview of generating functions and their applications Introduces the concepts at an appropriate level for beginners in applied science and engineering fields Demonstrates the various applications of generating functions using practical problems and examples

Autorentext

Rajan Chattamvelli, Ph.D., is a Professor in the School of Computer Science and Engineering at Amrita University, Amaravati. He has published more than 20 research articles in international journals, and his research interests include computational statistics, design of algorithms, parallel computing, cryptography, data mining, machine learning, and big data analytics.

Ramalingam Shanmugam, Ph.D., is an Honorary Professor in the School of Health Administration at Texas State University, San Marcos. He is the Editor-in-Chief of several journals including Advances in Life Sciences; Global Journal of Research and Review; Journal of Obesity and Metabolism; and the International Journal of Research in Medical Sciences . He has published more than 200 research articles and 120 conference papers. His research interests include theoretical and computational statistics, number theory, operations research, biostatistics, decision making, infectious disease modeling, patient risk management, cost-effective analysis and epidemiology.

Inhalt

Types of Generating Functions.- Operations on Generating Functions.- Generating Functions in Statistics.- Generating Functions in Mathematics.- Generating Functions in Computing.- Miscellaneous Applications of Generating Functions.