The aims and objectives of this book are to present a unified approach to the study of special functions of mathematics, which are ubiquitous and essential to a formulation of any physical or engineering problem in a mathematical format. In this detailed monograph, the second order Ordinary Differential Equation of Carl Friedrich Gauss is the starting point for the study of special functions. This is a simple, unified and novel approach to the treatment of the subject. The new feature in this presentation is that of the group theory associated with special functions.
Generalized Hypergeometric Functions: Transformations and group theoretical aspects outlines the important relationship between the Gauss hypergeometric equation and corresponding special functions. Each chapter details the application of group theory to the study of special functions and discusses various transformations, group theory, and their relevance in various applications. It is a relatively self-contained book that includes extensive introductory expositions of group theory.
Offering an original approach to the hypergeometric equation and related functions, this book is important for fundamental understanding of the mathematics underlying various aspects of physics, applied mathematics, and engineering. With the use of worked examples, proofs, summaries and references, this work can be used in various courses of study and research, and it is also useful for self-study.
Autorentext
With a PhD in theoretical physics from The Institute of Mathematical Sciences, Dr K Srinivasa Rao retired, from the same institute, as a senior professor. He has been a Humboldt Fellow and a visiting professor at various universities and research institutes worldwide and has contributed widely to both mathematics and theoretical physics. He has published a large number of books, journal articles and lecture notes, and he has also been very active in mathematics outreach activities highlighting the life and work of the Indian mathematician Ramanujan.
Dr Vasudevan Lakshminarayanan has a PhD from the University of California, Berkley, and is currently a professor at the University of Waterloo. Having worked in a vast number of areas including optical sciences, applied mathematics, electrical and biomedical engineering, ophthalmology and numerous other topics, Dr Lakshminarayanan has published more than 300 papers, journal articles and co-authored books.
Klappentext
In 1813, Gauss first outlined his studies of the hypergeometric series, which has been of great significance in the mathematical modelling of physical phenomena. This detailed monograph outlines the fundamental relationships between the hypergeometric function and special functions. In nine comprehensive chapters, Rao and Lakshminarayanan present a unified approach to the study of special functions of mathematics using group theory. This book offers fresh insight into various aspects of special functions and their relationship, utilizing transformations and group theory and their applications. It will lay the foundation for deeper understanding for both experienced researchers and novice students.
Inhalt
Dedications
Preface
Bios (not sure where?)
Acknowledgements
Chapter 1: Hypergeometric Series
Chapter 2: Group Theory : Basics
Chapter 3: Group Theory of the Kummer solutions of the Gauss differential equation
Chapter 4: Group theory of terminating and non-terminating 3F2(a; b; c; d; e; 1) transformations
Chapter 5: Angular Momentum and the Rotation group
Chapter 6: Angular Momentum recoupling and sets of 4F3(1)s
Chapter 7: Double and Triple Hypergeometric series
Chapter 8: Beta Integral Method and Hypergeometric transformations
Chapter 9: Gauss, Hypergeometric Series and Ramanujan
References