Theory of Hypergeometric Functions
Theory of Hypergeometric Functions

Author: Kazuhiko Aomoto

Publisher: Springer Science & Business Media

Published: 2011-05-21

Total Pages: 327

ISBN-13: 4431539387

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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.

Generalized Hypergeometric Functions
Generalized Hypergeometric Functions

Author: K. Srinivasa Rao

Publisher:

Published: 2018

Total Pages: 0

ISBN-13: 9780750314961

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"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.

Basic Hypergeometric Series and Applications
Basic Hypergeometric Series and Applications

Author: Nathan Jacob Fine

Publisher: American Mathematical Soc.

Published: 1988

Total Pages: 142

ISBN-13: 0821815245

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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.

Generalized Hypergeometric Functions
Generalized Hypergeometric Functions

Author: Bernard M. Dwork

Publisher:

Published: 1990

Total Pages: 206

ISBN-13:

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This monograph by one of the foremost experts on hypergeometric functions is concerned with the Boyarsky principle, developing a theory which is broad enough to encompass several of the most important hypergeometric functions.

Handbook of Mathematical Functions
Handbook of Mathematical Functions

Author: Milton Abramowitz

Publisher: Courier Corporation

Published: 1965-01-01

Total Pages: 1068

ISBN-13: 9780486612720

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An extensive summary of mathematical functions that occur in physical and engineering problems

Reflection Groups and Coxeter Groups
Reflection Groups and Coxeter Groups

Author: James E. Humphreys

Publisher: Cambridge University Press

Published: 1992-10

Total Pages: 222

ISBN-13: 9780521436137

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This graduate textbook presents a concrete and up-to-date introduction to the theory of Coxeter groups. The book is self-contained, making it suitable either for courses and seminars or for self-study. The first part is devoted to establishing concrete examples. Finite reflection groups acting on Euclidean spaces are discussed, and the first part ends with the construction of the affine Weyl groups, a class of Coxeter groups that plays a major role in Lie theory. The second part (which is logically independent of, but motivated by, the first) develops from scratch the properties of Coxeter groups in general, including the Bruhat ordering and the seminal work of Kazhdan and Lusztig on representations of Hecke algebras associated with Coxeter groups is introduced. Finally a number of interesting complementary topics as well as connections with Lie theory are sketched. The book concludes with an extensive bibliography on Coxeter groups and their applications.

An Introduction to Hypergeometric, Supertrigonometric, and Superhyperbolic Functions
An Introduction to Hypergeometric, Supertrigonometric, and Superhyperbolic Functions

Author: Xiao-Jun Yang

Publisher: Academic Press

Published: 2021-02-11

Total Pages: 502

ISBN-13: 0128241543

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An Introduction to Hypergeometric, Supertigonometric, and Superhyperbolic Functions gives a basic introduction to the newly established hypergeometric, supertrigonometric, and superhyperbolic functions from the special functions viewpoint. The special functions, such as the Euler Gamma function, the Euler Beta function, the Clausen hypergeometric series, and the Gauss hypergeometric have been successfully applied to describe the real-world phenomena that involve complex behaviors arising in mathematics, physics, chemistry, and engineering. Provides a historical overview for a family of the special polynomials Presents a logical investigation of a family of the hypergeometric series Proposes a new family of the hypergeometric supertrigonometric functions Presents a new family of the hypergeometric superhyperbolic functions