Hypergeometric Functions My Love
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Hypergeometric Functions My Love
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Author : Masaaki Yoshida
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Hypergeometric Functions My Love written by Masaaki Yoshida 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 2013-06-29 with Technology & Engineering categories.
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.
Theory Of Hypergeometric Functions
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Author : Kazuhiko Aomoto
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-21
Theory Of Hypergeometric Functions written by Kazuhiko Aomoto 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 2011-05-21 with Mathematics categories.
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.
Hypergeometric Functions Over Finite Fields
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Author : Jenny Fuselier
language : en
Publisher: American Mathematical Society
Release Date : 2022-11-10
Hypergeometric Functions Over Finite Fields written by Jenny Fuselier and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-10 with Mathematics categories.
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Arithmetic And Geometry Around Hypergeometric Functions
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Author : Rolf-Peter Holzapfel
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-28
Arithmetic And Geometry Around Hypergeometric Functions written by Rolf-Peter Holzapfel 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 2007-06-28 with Mathematics categories.
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.
Basic Hypergeometric Series
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Author : George Gasper
language : en
Publisher: Cambridge University Press
Release Date : 2004-10-04
Basic Hypergeometric Series written by George Gasper and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-04 with Mathematics categories.
This revised and expanded new edition will continue to meet the needs for an authoritative, up-to-date, self contained, and comprehensive account of the rapidly growing field of basic hypergeometric series, or q-series. Simplicity, clarity, deductive proofs, thoughtfully designed exercises, and useful appendices are among its strengths. The first five chapters cover basic hypergeometric series and integrals, whilst the next five are devoted to applications in various areas including Askey-Wilson integrals and orthogonal polynomials, partitions in number theory, multiple series, orthogonal polynomials in several variables, and generating functions. Chapters 9-11 are new for the second edition, the final chapter containing a simplified version of the main elements of the theta and elliptic hypergeometric series as a natural extension of the single-base q-series. Some sections and exercises have been added to reflect recent developments, and the Bibliography has been revised to maintain its comprehensiveness.
Hessian Polyhedra Invariant Theory And Appell Hypergeometric Functions
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Author : Lei Yang
language : en
Publisher: World Scientific
Release Date : 2018-03-13
Hessian Polyhedra Invariant Theory And Appell Hypergeometric Functions written by Lei Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-13 with Mathematics categories.
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 $mathfrak{G}’_{216}$. It provides another beautiful example on the fundamental unity of mathematics.
Multivariate Normal Distribution The Theory And Applications
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Author : Thu Pham-gia
language : en
Publisher: World Scientific
Release Date : 2021-05-05
Multivariate Normal Distribution The Theory And Applications written by Thu Pham-gia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-05 with Business & Economics categories.
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.
Gr Bner Deformations Of Hypergeometric Differential Equations
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Author : Mutsumi Saito
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Gr Bner Deformations Of Hypergeometric Differential Equations written by Mutsumi Saito 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.
In recent years, new algorithms for dealing with rings of differential operators have been discovered and implemented. A main tool is the theory of Gröbner bases, which is reexamined here from the point of view of geometric deformations. Perturbation techniques have a long tradition in analysis; Gröbner deformations of left ideals in the Weyl algebra are the algebraic analogue to classical perturbation techniques. The algorithmic methods introduced here are particularly useful for studying the systems of multidimensional hypergeometric PDEs introduced by Gelfand, Kapranov and Zelevinsky. The Gröbner deformation of these GKZ hypergeometric systems reduces problems concerning hypergeometric functions to questions about commutative monomial ideals, and leads to an unexpected interplay between analysis and combinatorics. This book contains a number of original research results on holonomic systems and hypergeometric functions, and raises many open problems for future research in this area.
Algebra Geometry And Software Systems
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Author : Michael Joswig
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Algebra Geometry And Software Systems written by Michael Joswig 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 2013-03-14 with Mathematics categories.
In many fields of modern mathematics specialised scientific software becomes increasingly important. Hence, tremendous effort is taken by numerous groups all over the world to develop appropriate solutions. This book contains 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. Therefore the volume's other focus is on solutions towards the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general framework for modular systems.
Arrangements Local Systems And Singularities
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Author : Fouad El Zein
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-14
Arrangements Local Systems And Singularities written by Fouad El Zein 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 2010-03-14 with Mathematics categories.
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.