Description |
1 online resource (xvi, 317 pages) |
Series |
Springer monographs in mathematics |
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Springer monographs in mathematics.
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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 |
Analysis |
wiskunde |
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mathematics |
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meetkunde |
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geometry |
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functionaalanalyse |
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functional analysis |
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Mathematics (General) |
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Wiskunde (algemeen) |
Bibliography |
Includes bibliographical references and index |
Notes |
English |
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Print version record |
In |
Springer eBooks |
Subject |
Hypergeometric functions.
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Geometry.
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geometry.
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Funciones hipergeométricas
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Hypergeometric functions
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Form |
Electronic book
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Author |
Kita, Michitake, -1995.
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LC no. |
2011923079 |
ISBN |
9784431539384 |
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4431539387 |
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4431539123 |
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9784431539124 |
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