TY  - BOOK
AU  - Srinivasa Rao,K.
AU  - Lakshminarayanan,Vasudevan
ED  - Institute of Physics, IOP - EBA (Great Britain),
TI  - Generalized hypergeometric functions: transformations and group theoretical aspects 
T2  - [IOP release 5]
SN  - 9780750314961
AV  - QA353.H9 S754 2018eb
U1  - 515.9 23
PY  - 2018///]
CY  - Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK)
PB  - IOP Publishing
KW  - Hypergeometric functions
KW  - Mathematical physics
KW  - bicssc
KW  - SCIENCE / Physics / Mathematical & Computational
KW  - bisacsh
N1  - "Version: 20181001"--Title page verso; Includes bibliographical references; 1. Hypergeometric series -- 1.1. Introduction -- 1.2. The Gauss differential equation -- 1.3. Special functions -- 1.4. Properties of the hypergeometric functions -- 1.5. A conjecture; 2. Group theory: basics -- 2.1. Introduction -- 2.2. Invariances, symmetries, and physics -- 2.3. Discrete groups -- 2.4. The symmetric group Sn -- 2.5. An interesting property of Sn -- 2.6. Representations of a group -- 2.7. Lie groups and Lie; 3. Group theory of the Kummer solutions of the Gauss differential equation -- 3.1. Introduction -- 3.2. The 24 solutions of the Gauss ODE -- 3.3. The Riemann equation; 4. Group theory of terminating and non-terminating 3F2(a, b, c; d, e; 1) transformations -- 4.1. Introduction -- 4.2. The Whipple notation -- 4.3. Terminating 3F2(1) series -- 4.4. Structure of GT and its irreps -- 4.5. Scaling the WE transforma; 5. Angular momentum and the rotation group -- 5.1. Introduction: historical -- 5.2. Angular momentum algebra -- 5.3. Representations of angular momentum operators -- 5.4. The rotation group -- 5.5. The 3F2(1) sets -- 5.6. Symmetries of the 3-j c; 6. Angular momentum recoupling and sets of 4F3(1)s -- 6.1. Introduction: historical -- 6.2. Addition of three angular momenta -- 6.3. Symmetries of the Racah coefficient -- 6.4. Two sets of 4F3(1)s -- 6.5. Inter-relationship of the two sets of 4; 7. Double and triple hypergeometric series -- 7.1. Introduction: a history -- 7.2. Multiple hypergeometric series -- 7.3. Definitions of the 9-j coefficient -- 7.4. Symmetries of the 9-j coefficient -- 7.5. The Jucys-Bandzaitis triple sum series; 8. Beta integral method and hypergeometric transformations -- 8.1. Introduction -- 8.2. Extensions of Euler's integral for 2F1(a, b; c; z) -- 8.3. The beta integral method -- 8.4. The algorithm -- 8.5. New single sum hypergeometric identities fr; 9. Gauss, hypergeometric series, and Ramanujan -- 9.1. Introduction -- 9.2. On some entries of Ramanujan on hypergeomtric series in his notebooks -- 9.3. Entry 43, in chapter XII of Ramanujan's Notebook 1 -- 9.4. The theorem of Rao, Berghe, and; Students (undergrad, grad, postgrad, and doctoral) and researchers needing special functions in their areas of study as well as practicing engineers needing a reference; Also available in print
N2  - 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 hypergeom
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ER  -