Theory of Hypergeometric Functions
(Sprache: Englisch)
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...
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Klappentext zu „Theory of Hypergeometric Functions “
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.
Inhaltsverzeichnis zu „Theory of Hypergeometric Functions “
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.
Bibliographische Angaben
- Autoren: Kazuhiko Aomoto , Michitake Kita
- 2011, 336 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Übersetzer: Kenji Iohara
- Verlag: Springer Tokyo
- ISBN-10: 4431539123
- ISBN-13: 9784431539124
- Erscheinungsdatum: 13.05.2011
Sprache:
Englisch
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