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E-book
Author Aomoto, Kazuhiko.

Title Theory of hypergeometric functions / Kazuhiko Aomoto, Michitake Kita ; with an appendix by Toshitake Kohno
Published Tokyo ; New York : Springer, [2011]
©2011
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Description 1 online resource (xvi, 317 pages)
Series Springer monographs in mathematics
Springer monographs in mathematics.
Contents 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
Summary 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
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Hypergeometric functions.
Form Electronic book
Author Kita, Michitake, -1995.
LC no. 2011923079
ISBN 4431539123
4431539387 (electronic bk.)
9784431539124
9784431539384 (electronic bk.)
(hard cover ; alk. paper)