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Generalized hypergeometric functions : transformations and group theoretical aspects /
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 comprehen...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) :
IOP Publishing,
[2018]
|
| Colección: | IOP (Series). Release 5.
IOP expanding physics. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Srinivasa Rao, K., |d 1942- |e author. | |
| 245 | 1 | 0 | |a Generalized hypergeometric functions : |b transformations and group theoretical aspects / |c K. Srinivasa Rao, Vasudevan Lakshminarayanan. |
| 264 | 1 | |a Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : |b IOP Publishing, |c [2018] | |
| 300 | |a 1 online resource (various pagings). | ||
| 336 | |a text |2 rdacontent | ||
| 337 | |a electronic |2 isbdmedia | ||
| 338 | |a online resource |2 rdacarrier | ||
| 490 | 1 | |a [IOP release 5] | |
| 490 | 1 | |a IOP expanding physics, |x 2053-2563 | |
| 500 | |a "Version: 20181001"--Title page verso. | ||
| 504 | |a Includes bibliographical references. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 algebras -- 2.8. Angular momentum and the rotation group -- 2.9. Compact Lie groups -- 2.10. Subgroups, cosets, invariant subgroups -- 2.11. Simple and semi-simple groups -- 2.12. Compact groups | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 transformation -- 4.6. Non-terminating 3F2(a, b, c; d, e; 1) series -- 4.7. Concluding remarks | |
| 505 | 8 | |a 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 coefficient -- 5.7. Inter-relationship between the sets of 3F2(1)s | |
| 505 | 8 | |a 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 4F3(1)s -- 6.6. Bargmann-Shelepin arrays -- 6.7. The set of Bailey transformations -- 6.8. Basis states and symmetries of the 6-j coefficient | |
| 505 | 8 | |a 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 -- 7.6. Stretched 9-j coefficients -- 7.7. A general transformation formula -- 7.8. Transformation formulas for F⁰:3;4 ₁:1;2 -- 7.9. Transformation formulas for F¹:2;2 ₀:2;2 -- 7.10. Some summation formulas | |
| 505 | 8 | |a 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 from old ones | |
| 505 | 8 | |a 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 Krattenthaler -- 9.5. Observations and concluding remarks -- 9.6. Epilogue. | |
| 520 | 3 | |a 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, Dr. Rao and Dr. Lakshminarayanan present a unified approach to the study of special functions of mathematics using Group theory. The 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 by both experienced researchers and novice students. | |
| 521 | |a Students (undergrad, grad, postgrad, and doctoral) and researchers needing special functions in their areas of study as well as practicing engineers needing a reference. | ||
| 530 | |a Also available in print. | ||
| 538 | |a Mode of access: World Wide Web. | ||
| 538 | |a System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader. | ||
| 545 | |a Dr. K Srinivasa Rao. 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. He has also been very active in math outreach activities highlighting the life and work of the Indian mathematician Ramanujan. Dr. Vasudevan Lakshminarayanan has a PhD in from the University of California at Berkley and is currently a professor at The University of Waterloo. Having worked on a vast number of areas including optical sciences, applied math, electrical and biomedical engineering, ophthalmology and numerous other topics, Dr. Lakshminarayanan has published over 300 papers, journal articles, and co-authored books. | ||
| 588 | 0 | |a Title from PDF title page (viewed on November 8, 2018). | |
| 650 | 0 | |a Hypergeometric functions. | |
| 650 | 7 | |a Mathematical physics. |2 bicssc | |
| 650 | 7 | |a SCIENCE / Physics / Mathematical & Computational. |2 bisacsh | |
| 700 | 1 | |a Lakshminarayanan, Vasudevan, |e author. | |
| 710 | 2 | |a Institute of Physics (Great Britain), |e publisher. | |
| 776 | 0 | 8 | |i Print version: |z 9780750314947 |
| 830 | 0 | |a IOP (Series). |p Release 5. | |
| 830 | 0 | |a IOP expanding physics. | |
| 856 | 4 | 0 | |u https://iopscience.uam.elogim.com/book/978-0-7503-1496-1 |z Texto completo |