This book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. It shows that hypergeometric integrals generally satisfy holonomic system of linear differential equations.

Reader will understand clearly multidimensional hypergeometric function as a natural extension of the classical one from viewpoint of integrals A quick introduction to rational de Rham cohomology due to A.Grothendieck and P.Deligne and also to holonomic differential equations (or Gauss-Manin connection) and difference equations associated with hypergeometric functions Application of hypergeometric functions to several analytic or geometric problems Includes supplementary material: sn.pub/extras

Inhalt
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.