Theory of Hypergeometric Functions

by Kazuhiko Aomoto, Michitake Kita, Kenji Iohara (Translator)

Overview

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.

Product Details

ISBN-13:	9784431540878
Publisher:	Springer Japan
Publication date:	07/14/2013
Series:	Springer Monographs in Mathematics
Edition description:	2011
Pages:	320
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

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.