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Theory of Hypergeometric Functions

Theory of Hypergeometric Functions by Kazuhiko Aomoto
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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.
Springer Japan; May 2011
326 pages; ISBN 9784431539384
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Title: Theory of Hypergeometric Functions
Author: Kazuhiko Aomoto; Michitake Kita; Toshitake Kohno; Kenji Iohara
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