Lie Theory Matrix Theory And Special Functions
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Lie Theory Matrix Theory And Special Functions
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Author : Dwivedi Ravi
language : en
Publisher:
Release Date : 2022-11-06
Lie Theory Matrix Theory And Special Functions written by Dwivedi Ravi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-06 with categories.
In this chapter, we give a brief review of the theory of special functions, special matrix functions and representation theory of Lie algebras that will be needed in the subsequent chapters. The theory of special functions has been enriched by the works of Euler, Gauss, Kummer, Riemann and Ramanujan, to name a few. For a detailed study of the subject, we refer to Bailey [5], Erdelyi, Magnus, Oberhettinger and Tricomi [18], Rainville [64], Slater [75], Exton [20]-[22], Srivastava and Manocha [80], Srivastava and Karlsson [81], Gasper and Rahman [28] and Andrews, Askey and Roy [3].
Lie Theory And Special Functions
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Author : Miller
language : en
Publisher: Academic Press
Release Date : 1968
Lie Theory And Special Functions written by Miller and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.
Lie Theory and Special Functions
Matrix Methods And Fractional Calculus
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Author : Arak M Mathai
language : en
Publisher: World Scientific
Release Date : 2017-11-10
Matrix Methods And Fractional Calculus written by Arak M Mathai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-10 with Mathematics categories.
Fractional calculus in terms of mathematics and statistics and its applications to problems in natural sciences is NOT yet part of university teaching curricula. This book is one attempt to provide an approach to include topics of fractional calculus into university curricula. Additionally the material is useful for people who do research work in the areas of special functions, fractional calculus, applications of fractional calculus, and mathematical statistics.
Symmetries And Integrability Of Difference Equations
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Author : Decio Levi
language : en
Publisher: American Mathematical Soc.
Release Date :
Symmetries And Integrability Of Difference Equations written by Decio Levi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Representation Theory And Noncommutative Harmonic Analysis Ii
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Author : A.A. Kirillov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Representation Theory And Noncommutative Harmonic Analysis Ii written by A.A. Kirillov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
At first only elementary functions were studied in mathematical analysis. Then new functions were introduced to evaluate integrals. They were named special functions: integral sine, logarithms, the exponential function, the prob ability integral and so on. Elliptic integrals proved to be the most important. They are connected with rectification of arcs of certain curves. The remarkable idea of Abel to replace these integrals by the corresponding inverse functions led to the creation of the theory of elliptic functions. They are doubly periodic functions of a complex variable. This periodicity has led to consideration of the lattice of periods and to linear-fractional trans formations of the complex plane which leave this lattice invariant. The group of these transformations is isomorphic to the quotient group of the group 8L(2, Z) of unimodular matrices of the second order with integral elements with respect to its center. Investigation of properties of elliptic functions led to the study of automorphic functions and forms. This gave the first connec tion between the theory of groups and this important class of functions. The further development of the theory of automorphic functions was related to geometric concepts connected with the fact that the group of linear-fractional transformations with real elements can be realized as the group of motions of th the Lobachevskij plane. We also note that at the beginning of the 19 century Gauss used the group 8L(2, Z) in his papers on the theory of indeterminate quadratic forms.
Special Functions Group Theoretical Aspects And Applications
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Author : R.A. Askey
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Special Functions Group Theoretical Aspects And Applications written by R.A. Askey and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Approach your problems from It isn't that they can't see the right end and begin with the solution. the answers. Then one day, It is that they can't see the perhaps you will find the problem. final question. G.K. Chesterton. The Scandal 'The Hermit Clad in Crane of Father Brown 'The Point of Feathers' in R. van Gulik's a Pin'. The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging SUbdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Representation Of Lie Groups And Special Functions
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Author : N. Ja. Vilenkin
language : en
Publisher:
Release Date : 2014-01-15
Representation Of Lie Groups And Special Functions written by N. Ja. Vilenkin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Integrable Systems Quantum Groups And Quantum Field Theories
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Author : Alberto Ibort
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integrable Systems Quantum Groups And Quantum Field Theories written by Alberto Ibort and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
In many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics. This book contains the lectures delivered at the NATO-ASI Summer School on `Recent Problems in Mathematical Physics' held at Salamanca, Spain (1992), offering a pedagogical and updated approach to some of the problems that have been at the heart of these events. Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the book. Apart from these, traditional and new problems in quantum gravity are reviewed. Other contributions to the School included in the book range from symmetries in partial differential equations to geometrical phases in quantum physics. The book is addressed to researchers in the fields covered, PhD students and any scientist interested in obtaining an updated view of the subjects.
Nuclear Science Abstracts
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Author :
language : en
Publisher:
Release Date : 1969
Nuclear Science Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Nuclear energy categories.
Engineering Applications Of Noncommutative Harmonic Analysis
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Author : Gregory S. Chirikjian
language : en
Publisher: CRC Press
Release Date : 2021-02-25
Engineering Applications Of Noncommutative Harmonic Analysis written by Gregory S. Chirikjian and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-25 with Mathematics categories.
First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.