Generalized Hypergeometric Functions explores the way in which hypergeometric functions are interlinked with special functions, and it uses group theory to illustrate these relationships. The application of group theory to the study of special functions is a relatively new approach to the subject area. It is a departure from most of the standard text books, which deal with the special functions as disjointed chapters, with each chapter dealing with the properties of the given special function.
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.
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