Theory Of Hypergeometric Functions PDF Download
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Author | : Kazuhiko Aomoto |
Publisher | : Springer Science & Business Media |
Total Pages | : 327 |
Release | : 2011-05-21 |
Genre | : Mathematics |
ISBN | : 4431539387 |
Download Theory of Hypergeometric Functions Book in PDF, ePub and Kindle
This book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. Starting from an integrand which is a product of powers of polynomials, integrals are explained, in an open affine space, as a pair of twisted de Rham cohomology and its dual over the coefficients of local system. It is shown that hypergeometric integrals generally satisfy a holonomic system of linear differential equations with respect to the coefficients of polynomials and also satisfy a holonomic system of linear difference equations with respect to the exponents. These are deduced from Grothendieck-Deligne’s rational de Rham cohomology on the one hand, and by multidimensional extension of Birkhoff’s classical theory on analytic difference equations on the other.
Author | : Nathan Jacob Fine |
Publisher | : American Mathematical Soc. |
Total Pages | : 142 |
Release | : 1988 |
Genre | : Mathematics |
ISBN | : 0821815245 |
Download Basic Hypergeometric Series and Applications Book in PDF, ePub and Kindle
The theory of partitions, founded by Euler, has led in a natural way to the idea of basic hypergeometric series, also known as Eulerian series. These series were first studied systematically by Heine, but many early results are attributed to Euler, Gauss, and Jacobi. This book provides a simple approach to basic hypergeometric series.
Author | : K. Srinivasa Rao |
Publisher | : |
Total Pages | : 0 |
Release | : 2018 |
Genre | : Hypergeometric functions |
ISBN | : 9780750314961 |
Download Generalized Hypergeometric Functions Book in PDF, ePub and Kindle
"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." -- Prové de l'editor.
Author | : Herbert Buchholz |
Publisher | : Springer Science & Business Media |
Total Pages | : 255 |
Release | : 2013-11-22 |
Genre | : Science |
ISBN | : 3642883966 |
Download The Confluent Hypergeometric Function Book in PDF, ePub and Kindle
The subject of this book is the higher transcendental function known as the confluent hypergeometric function. In the last two decades this function has taken on an ever increasing significance because of its use in the application of mathematics to physical and technical problems. There is no doubt that this trend will continue until the general theory of confluent hypergeometric functions becomes familiar to the majority of physicists in much the same way as the cylinder functions, which were previously less well known, are now used in many engineering and physical problems. This book is intended to further this development. The important practical significance of the functions which are treated hardly demands an involved discussion since they include, as special cases, a number of simpler special functions which have long been the everyday tool of the physicist. It is sufficient to mention that these include, among others, the logarithmic integral, the integral sine and cosine, the error integral, the Fresnel integral, the cylinder functions and the cylinder function in parabolic cylindrical coordinates. For anyone who puts forth the effort to study the confluent hypergeometric function in more detail there is the inestimable advantage of being able to understand the properties of other functions derivable from it. This gen eral point of view is particularly useful in connection with series ex pansions valid for values of the argument near zero or infinity and in connection with the various integral representations.
Author | : George Gasper |
Publisher | : |
Total Pages | : 456 |
Release | : 2011-02-25 |
Genre | : Mathematics |
ISBN | : 0511889186 |
Download Basic Hypergeometric Series Book in PDF, ePub and Kindle
Significant revision of classic reference in special functions.
Author | : James B. Seaborn |
Publisher | : Springer Science & Business Media |
Total Pages | : 261 |
Release | : 2013-04-09 |
Genre | : Science |
ISBN | : 1475754434 |
Download Hypergeometric Functions and Their Applications Book in PDF, ePub and Kindle
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe matical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface A wide range of problems exists in classical and quantum physics, engi neering, and applied mathematics in which special functions arise. The procedure followed in most texts on these topics (e. g. , quantum mechanics, electrodynamics, modern physics, classical mechanics, etc. ) is to formu late the problem as a differential equation that is related to one of several special differential equations (Hermite's, Bessel's, Laguerre's, Legendre's, etc. ).
Author | : Mutsumi Saito |
Publisher | : Springer Science & Business Media |
Total Pages | : 261 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 366204112X |
Download Gröbner Deformations of Hypergeometric Differential Equations Book in PDF, ePub and Kindle
The theory of Gröbner bases is a main tool for dealing with rings of differential operators. This book reexamines the concept of Gröbner bases from the point of view of geometric deformations. The algorithmic methods introduced in this book are particularly useful for studying the systems of multidimensional hypergeometric PDE's introduced by Gelfand, Kapranov, and Zelevinsky. A number of original research results are contained in the book, and many open problems are raised for future research in this rapidly growing area of computational mathematics.
Author | : Lucy Joan Slater |
Publisher | : |
Total Pages | : 0 |
Release | : 1993 |
Genre | : |
ISBN | : |
Download Generalized Hypergeometric Functions Book in PDF, ePub and Kindle
Author | : Masaaki Yoshida |
Publisher | : Springer Science & Business Media |
Total Pages | : 301 |
Release | : 2013-06-29 |
Genre | : Technology & Engineering |
ISBN | : 3322901661 |
Download Hypergeometric Functions, My Love Book in PDF, ePub and Kindle
The classical story - of the hypergeometric functions, the configuration space of 4 points on the projective line, elliptic curves, elliptic modular functions and the theta functions - now evolves, in this book, to the story of hypergeometric funktions in 4 variables, the configuration space of 6 points in the projective plane, K3 surfaces, theta functions in 4 variables. This modern theory has been established by the author and his collaborators in the 1990's; further development to different aspects is expected. It leads the reader to a fascinating 4-dimensional world. The author tells the story casually and visually in a plain language, starting form elementary level such as equivalence relations, the exponential function, ... Undergraduate students should be able to enjoy the text.
Author | : George E. Andrews |
Publisher | : Springer |
Total Pages | : 736 |
Release | : 2018-02-01 |
Genre | : Mathematics |
ISBN | : 3319683764 |
Download Analytic Number Theory, Modular Forms and q-Hypergeometric Series Book in PDF, ePub and Kindle
Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory. Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.