Description 
1 online resource (xvi, 317 pages) 
Series 
Springer monographs in mathematics 

Springer monographs in mathematics.

Contents 
1 Introduction: the EulerGauss 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 
Summary 
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 GrothendieckDeligne'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 
Bibliography 
Includes bibliographical references and index 
Notes 
Print version record 
Subject 
Hypergeometric functions.

Form 
Electronic book

Author 
Kita, Michitake, 1995.

LC no. 
2011923079 
ISBN 
4431539123 

4431539387 (electronic bk.) 

9784431539124 

9784431539384 (electronic bk.) 

(hard cover ; alk. paper) 
