(DOWNLOAD) "Theory of Hypergeometric Functions" by Kazuhiko Aomoto & Michitake Kita * eBook PDF Kindle ePub Free

eBook details

Title: Theory of Hypergeometric Functions
Author : Kazuhiko Aomoto & Michitake Kita
Release Date : January 21, 2011
Genre: Mathematics,Books,Science & Nature,
Pages : * pages
Size : 6795 KB

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.