Theory of Hypergeometric Functions
1st Edition
Published on 21. May 2011
XVI, 320 pages
978-4-431-53938-4 (ISBN)
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.
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Kazuhiko Aomoto | Michitake Kita
Theory of Hypergeometric Functions
Book
07/2013
Springer
€96.29
Shipment within 10-15 days
Kazuhiko Aomoto | Michitake Kita
Theory of Hypergeometric Functions
Book
05/2011
1st Edition
Springer
€139.09
Shipment within 10-15 days
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Content
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.
