Theory of Hypergeometric Functions (Springer Monographs in Mathematics) [9784431540878]

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.

The book, Theory of Hypergeometric Functions (Springer Monographs in Mathematics) [Bulk, Wholesale, Quantity] ISBN#9784431540878 in Paperback by Kazuhiko Aomoto, Michitake Kita may be ordered in bulk quantities. Minimum starts at 25 copies. Availability based on publisher status and quantity being ordered.