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Theory of Hypergeometric Functions

Theory of Hypergeometric Functions
Catalogue Information
Field name Details
Dewey Class 516
Title Theory of Hypergeometric Functions (EB) / by Kazuhiko Aomoto, Michitake Kita.
Author Aomoto, Kazuhiko
Added Personal Name Kita, Michitake
Other name(s) SpringerLink (Online service)
Publication Tokyo : : Springer Japan :
: Imprint: Springer, , 2011.
Physical Details XVI, 320 p. : online resource.
Series Springer monographs in mathematics 1439-7382
ISBN 9784431539384
Summary Note 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-Deligneâs rational de Rham cohomology on the one hand, and by multidimensional extension of Birkhoffâs classical theory on analytic difference equations on the other.:
Contents note 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.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
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