Overview
- Provides broad exposure to commonly used techniques of combinatorial mathematics
- Introduces commonly encountered generating functions for researchers working in economics, finance, and statistics
- Developed for beginners in science and engineering fields to help understand single-variable generating functions
Part of the book series: Synthesis Lectures on Engineering, Science, and Technology (SLEST)
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Table of contents (4 chapters)
Keywords
- Generating Function Applications
- Generating Functions in Statistics
- Operations on Generating Functions
- New Generating Functions
- Mean Deviation Generating Functions
- Survival Function Generating Functions
- Pochhammer Generating Functions
- Inverse Relations
- Combinatorics
- Continuous Algebraic Functions
- Reliability
- Bioinformatics
- Analysis of Algorithms
- Number Theory
About this book
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.
Authors and Affiliations
About the authors
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, operationsresearch, biostatistics, decision making, and epidemiology.
Bibliographic Information
Book Title: Generating Functions in Engineering and the Applied Sciences
Authors: Rajan Chattamvelli, Ramalingam Shanmugam
Series Title: Synthesis Lectures on Engineering, Science, and Technology
DOI: https://doi.org/10.1007/978-3-031-21143-0
Publisher: Springer Cham
eBook Packages: Synthesis Collection of Technology (R0), eBColl Synthesis Collection 12
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-21142-3Published: 02 January 2023
Softcover ISBN: 978-3-031-21145-4Published: 03 January 2024
eBook ISBN: 978-3-031-21143-0Published: 01 January 2023
Series ISSN: 2690-0300
Series E-ISSN: 2690-0327
Edition Number: 2
Number of Pages: XIV, 119
Number of Illustrations: 1 b/w illustrations, 3 illustrations in colour
Topics: Applied Statistics, Discrete Mathematics, Engineering Mathematics, Financial Engineering, Macroeconomics/Monetary Economics//Financial Economics, Number Theory