
Theory of Hypergeometric Functions
Springer (Publisher)
Published on 15. July 2013
Book
Paperback/Softback
XVI, 320 pages
978-4-431-54087-8 (ISBN)
Description
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.
More details
Series
Edition
2011 ed.
Language
English
Place of publication
Tokyo
Japan
Target group
Professional and scholarly
Professional/practitioner
Illustrations
XVI, 320 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 19 mm
Weight
511 gr
ISBN-13
978-4-431-54087-8 (9784431540878)
DOI
10.1007/978-4-431-53938-4
Schweitzer Classification
Other editions
Additional editions

Kazuhiko Aomoto | Michitake Kita
Theory of Hypergeometric Functions
E-Book
05/2011
1st Edition
Springer
€96.29
Available for download

Kazuhiko Aomoto | Michitake Kita
Theory of Hypergeometric Functions
Book
05/2011
1st Edition
Springer
€139.09
Shipment within 10-15 days
Persons
Content
1 Introduction: the Euler-Gauss Hypergeometric Function.- 2 Representation of Complex Integrals and Twisted de Rham Cohomologies.- 3 Hypergeometric functions over Grassmannians.- 4 Holonomic Difference Equations and Asymptotic Expansion References Index.