Generalized Hypergeometric Functions (eBook)

Transformations and group theoretical aspects

K Srinivasa Rao, Vasudevan Lakshminarayanan (Autoren)

eBook Download: EPUB

2018
200 Seiten
Institute of Physics Publishing (Verlag)
978-0-7503-1496-1 (ISBN)

Infos

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.

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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. 
 

Autor

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.

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

Produkt-Details

• Erscheint lt. Verlag: 24.10.2018
• Reihe/Serie: IOP Expanding Physics
• Reihe/Serie: IOP Expanding Physics
• Reihe/Serie: ISSN
• Reihe/Serie: ISSN
• Zusatzinfo: With figures in colour and black and white
• Verlagsort: Bristol
• Sprache: englisch
• Themenwelt: Naturwissenschaften
• Schlagworte: quantum theory, special functions, coupling, recoupling, differential equations,
• ISBN-10: 0-7503-1496-6 / 0750314966
• ISBN-13: 978-0-7503-1496-1 / 9780750314961