Theory of Hypergeometric Functions

By Michitake Kita and Kazuhiko Aomoto

Book 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.

• Format: Paperback
• Language: English
• ISBN: 4431540873
• ISBN13: 9784431540878
• Release Date: July 2013
• Publisher: Springer
• Length: 320 Pages
• Weight: 1.06 lbs.
• Dimensions: 0.7" x 6.2" x 9.2"