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Generalized Hypergeometric Functions

Transformations and group theoretical aspects
K Srinivasa Rao, Dr Vasudevan Lakshminarayanan


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.   

About Editors

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.

Table of Contents





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



Hardback ISBN: 9780750314947

Ebook ISBN: 9780750314961

DOI: 10.1088/978-0-7503-1496-1

Publisher: Institute of Physics Publishing


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