Theory of Hypergeometric Functions

• Main Authors: Aomoto, Kazuhiko (Author), Kita, Michitake (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Tokyo : Springer Japan : Imprint: Springer, 2011.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Functional analysis.; Geometry.; Functional Analysis.

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 du...

Table of Contents:

• 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.