Generating Functions in Engineering and the Applied Sciences

ISBN-13: 9783031211423 / Angielski / Twarda / 2023 / 119 str.

Rajan Chattamvelli; Ramalingam Shanmugam

Opis

Generating function (GF) is a mathematical technique to concisely represent a known ordered sequence into a simple continuous algebraic function in dummy variable(s). This Second Edition introduces commonly encountered generating functions (GFs) in engineering and applied sciences, such as ordinary GF (OGF), exponential GF (EGF), as also Dirichlet GF (DGF), Lambert GF (LGF), Logarithmic GF (LogGF), Hurwitz GF (HGF), Mittag-Lefler GF (MLGF), etc.  This book is intended mainly for beginners in applied science and engineering fields to help them understand single-variable GFs and illustrate how to apply them in various practical problems.  Specifically, the book discusses probability GFs (PGF),  moment and cumulant GFs (MGF, CGF), mean deviation GFs (MDGF), survival function GFs (SFGF), rising and falling factorial GFs, factorial moment, and inverse factorial moment GFs.  Applications of GFs in algebra, analysis of algorithms, bioinformatics, combinatorics, economics, finance, genomics, geometry, graph theory, management, number theory, polymer chemistry, reliability, statistics and structural engineering have been added to this new edition. This book is written in such a way that readers who do not have prior knowledge of the topic can easily follow through the chapters and apply the lessons learned in their respective disciplines.

Spis treści

Types of Generating Functions.- Operations on Generating Functions.- Generating Functions in Statistics.- Applications of Generating Functions.- Bibliography.

O autorze

Rajan Chattamvelli, Ph.D., is a Professor in the School of Advanced Sciences at Vellore Institute of Technology, Tamil Nadu, India.  He has published more than 20 research articles in international journals, and his research interests include computational statistics, design of algorithms, parallel computing, data mining, machine learning, blockchain, combinatorics, 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 four 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.  Dr.  Shanmugam's research interests include theoretical and computational statistics, number theory, operations research, biostatistics, decision making, and epidemiology.

Blurb

Generating function (GF) is a mathematical technique to concisely represent a known ordered sequence into a simple continuous algebraic function in dummy variable(s). This Second Edition introduces commonly encountered generating functions (GFs) in engineering and applied sciences, such as ordinary GF (OGF), exponential GF (EGF), as also Dirichlet GF (DGF), Lambert GF (LGF), Logarithmic GF (LogGF), Hurwitz GF (HGF), Mittag-Lefler GF (MLGF), etc.  This book is intended mainly for beginners in applied science and engineering fields to help them understand single-variable GFs and illustrate how to apply them in various practical problems.  Specifically, the book discusses probability GFs (PGF),  moment and cumulant GFs (MGF, CGF), mean deviation GFs (MDGF), survival function GFs (SFGF), rising and falling factorial GFs, factorial moment, and inverse factorial moment GFs.  Applications of GFs in algebra, analysis of algorithms, bioinformatics, combinatorics, economics, finance, genomics, geometry, graph theory, management, number theory, polymer chemistry, reliability, statistics and structural engineering have been added to this new edition. This book is written in such a way that readers who do not have prior knowledge of the topic can easily follow through the chapters and apply the lessons learned in their respective disciplines.

1. Provides broad exposure to commonly used techniques of combinatorial mathematics

2. Introduces commonly encountered generating functions for researchers working in economics, finance, and statistics

3.Developed for beginners in science and engineering fields to help understand single-variable generating functions