Hypergeometric Functions My Love

Author : Masaaki Yoshida
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 52,5 Mb
Release : 2013-06-29
Category : Technology & Engineering
ISBN : 9783322901668

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Hypergeometric Functions, My Love by Masaaki Yoshida Pdf

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 Gasper,Mizan Rahman
Publisher : Unknown
Page : 456 pages
File Size : 50,5 Mb
Release : 2011-02-25
Category : Mathematics
ISBN : 9780511889189

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Basic Hypergeometric Series by George Gasper,Mizan Rahman Pdf

Significant revision of classic reference in special functions.

Author : Rolf-Peter Holzapfel,Muhammed Uludag,M. Yoshida
Publisher : Springer Science & Business Media
Page : 437 pages
File Size : 43,9 Mb
Release : 2007-06-28
Category : Mathematics
ISBN : 9783764382841

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Arithmetic and Geometry Around Hypergeometric Functions by Rolf-Peter Holzapfel,Muhammed Uludag,M. Yoshida Pdf

This volume comprises lecture notes, survey and research articles originating from the CIMPA Summer School Arithmetic and Geometry around Hypergeometric Functions held at Galatasaray University, Istanbul, June 13-25, 2005. It covers a wide range of topics related to hypergeometric functions, thus giving a broad perspective of the state of the art in the field.

Author : Kazuhiko Aomoto,Michitake Kita
Publisher : Springer Science & Business Media
Page : 327 pages
File Size : 44,8 Mb
Release : 2011-05-21
Category : Mathematics
ISBN : 9784431539384

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Theory of Hypergeometric Functions by Kazuhiko Aomoto,Michitake Kita Pdf

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 : Jenny Fuselier,Ling Long,Ravi Ramakrishna,Holly Swisher,Fang-Ting Tu
Publisher : American Mathematical Society
Page : 138 pages
File Size : 45,6 Mb
Release : 2022-11-10
Category : Mathematics
ISBN : 9781470454333

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Hypergeometric Functions Over Finite Fields by Jenny Fuselier,Ling Long,Ravi Ramakrishna,Holly Swisher,Fang-Ting Tu Pdf

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Author : Yang Lei
Publisher : World Scientific
Page : 316 pages
File Size : 48,6 Mb
Release : 2018-03-13
Category : Mathematics
ISBN : 9789813209497

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Hessian Polyhedra, Invariant Theory and Appell Hypergeometric Functions by Yang Lei Pdf

Our book gives the complex counterpart of Klein's classic book on the icosahedron. We show that the following four apparently disjoint theories: the symmetries of the Hessian polyhedra (geometry), the resolution of some system of algebraic equations (algebra), the system of partial differential equations of Appell hypergeometric functions (analysis) and the modular equation of Picard modular functions (arithmetic) are in fact dominated by the structure of a single object, the Hessian group 𝔊′216. It provides another beautiful example on the fundamental unity of mathematics.

Author : Thu Pham-gia
Publisher : World Scientific
Page : 494 pages
File Size : 54,9 Mb
Release : 2021-05-05
Category : Business & Economics
ISBN : 9789811235306

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Multivariate Normal Distribution, The: Theory And Applications by Thu Pham-gia Pdf

This book provides the reader with user-friendly applications of normal distribution. In several variables it is called the multinormal distribution which is often handled using matrices for convenience. The author seeks to make the arguments less abstract and hence, starts with the univariate case and moves progressively toward the vector and matrix cases. The approach used in the book is a gradual one, going from one scalar variable to a vector variable and to a matrix variable. The author presents the unified aspect of normal distribution, as well as addresses several other issues, including random matrix theory in physics. Other well-known applications, such as Herrnstein and Murray's argument that human intelligence is substantially influenced by both inherited and environmental factors, will be discussed in this book. It is a better predictor of many personal dynamics — including financial income, job performance, birth out of wedlock, and involvement in crime — than are an individual's parental socioeconomic status, or education level, and deserve to be mentioned and discussed.

Author : Lucy Joan Slater
Publisher : Unknown
Page : 272 pages
File Size : 52,6 Mb
Release : 1960
Category : Mathematics
ISBN : STANFORD:36105030096007

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Confluent Hypergeometric Functions by Lucy Joan Slater Pdf

Author : James B. Seaborn
Publisher : Springer Science & Business Media
Page : 261 pages
File Size : 43,7 Mb
Release : 2013-04-09
Category : Science
ISBN : 9781475754438

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Hypergeometric Functions and Their Applications by James B. Seaborn Pdf

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 : Marko Petkovsek,Herbert S Wilf,Doron Zeilberger
Publisher : CRC Press
Page : 224 pages
File Size : 41,5 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 9781439864500

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A = B by Marko Petkovsek,Herbert S Wilf,Doron Zeilberger Pdf

This book is of interest to mathematicians and computer scientists working in finite mathematics and combinatorics. It presents a breakthrough method for analyzing complex summations. Beautifully written, the book contains practical applications as well as conceptual developments that will have applications in other areas of mathematics. From the table of contents: * Proof Machines * Tightening the Target * The Hypergeometric Database * The Five Basic Algorithms: Sister Celine's Method, Gosper&'s Algorithm, Zeilberger's Algorithm, The WZ Phenomenon, Algorithm Hyper * Epilogue: An Operator Algebra Viewpoint * The WWW Sites and the Software (Maple and Mathematica) Each chapter contains an introduction to the subject and ends with a set of exercises.

Author : A. M. Mathai,R. K. Saxena
Publisher : Unknown
Page : 340 pages
File Size : 40,8 Mb
Release : 1973
Category : Mathematics
ISBN : CORNELL:31924000210421

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Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences by A. M. Mathai,R. K. Saxena Pdf

Author : Lucy Joan Slater
Publisher : Unknown
Page : 287 pages
File Size : 46,8 Mb
Release : 1966
Category : Hypergeometric functions
ISBN : 0608116157

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Generalized Hypergeometric Functions by Lucy Joan Slater Pdf

Author : R. Wong
Publisher : Academic Press
Page : 561 pages
File Size : 50,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483220710

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Asymptotic Approximations of Integrals by R. Wong Pdf

Asymptotic Approximations of Integrals deals with the methods used in the asymptotic approximation of integrals. Topics covered range from logarithmic singularities and the summability method to the distributional approach and the Mellin transform technique for multiple integrals. Uniform asymptotic expansions via a rational transformation are also discussed, along with double integrals with a curve of stationary points. For completeness, classical methods are examined as well. Comprised of nine chapters, this volume begins with an introduction to the fundamental concepts of asymptotics, followed by a discussion on classical techniques used in the asymptotic evaluation of integrals, including Laplace's method, Mellin transform techniques, and the summability method. Subsequent chapters focus on the elementary theory of distributions; the distributional approach; uniform asymptotic expansions; and integrals which depend on auxiliary parameters in addition to the asymptotic variable. The book concludes by considering double integrals and higher-dimensional integrals. This monograph is intended for graduate students and research workers in mathematics, physics, and engineering.

Author : Michael Joswig,Nobuki Takayama
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 45,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662051481

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Algebra, Geometry and Software Systems by Michael Joswig,Nobuki Takayama Pdf

A collection of surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gröbner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. This is why the volume also focuses on solutions to the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.

Author : Fouad El Zein,Alexander I. Suciu,Meral Tosun,Muhammed Uludag,Sergey Yuzvinsky
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 55,5 Mb
Release : 2010-03-14
Category : Mathematics
ISBN : 9783034602099

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Arrangements, Local Systems and Singularities by Fouad El Zein,Alexander I. Suciu,Meral Tosun,Muhammed Uludag,Sergey Yuzvinsky Pdf

This volume comprises the Lecture Notes of the CIMPA/TUBITAK Summer School Arrangements, Local systems and Singularities held at Galatasaray University, Istanbul during June 2007. The volume is intended for a large audience in pure mathematics, including researchers and graduate students working in algebraic geometry, singularity theory, topology and related fields. The reader will find a variety of open problems involving arrangements, local systems and singularities proposed by the lecturers at the end of the school.