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02595nam a22004695i 4500 |
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978-4-431-53938-4 |
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DE-He213 |
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20130725210750.0 |
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cr nn 008mamaa |
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110521s2011 ja | s |||| 0|eng d |
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|a 9784431539384
|9 978-4-431-53938-4
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|a 10.1007/978-4-431-53938-4
|2 doi
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|a QA440-699
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|a MAT012000
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|a 516
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|a Aomoto, Kazuhiko.
|e author.
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|a Theory of Hypergeometric Functions
|h [electronic resource] /
|c by Kazuhiko Aomoto, Michitake Kita.
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|a Tokyo :
|b Springer Japan :
|b Imprint: Springer,
|c 2011.
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|a XVI, 320 p.
|b online resource.
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|a text
|b txt
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|a computer
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|2 rdamedia
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|a online resource
|b cr
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|a text file
|b PDF
|2 rda
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|a Springer Monographs in Mathematics,
|x 1439-7382
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|a 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.
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|a 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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|a Mathematics.
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|a Functional analysis.
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|a Geometry.
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|a Mathematics.
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|a Geometry.
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|a Functional Analysis.
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|a Kita, Michitake.
|e author.
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9784431539124
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| 830 |
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|a Springer Monographs in Mathematics,
|x 1439-7382
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|u http://dx.doi.org/10.1007/978-4-431-53938-4
|z Full Text via HEAL-Link
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|a ZDB-2-SMA
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| 950 |
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|a Mathematics and Statistics (Springer-11649)
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