Theory of Hypergeometric Functions [recurso electrónico] / by Kazuhiko Aomoto, Michitake Kita.
Tipo de material: TextoSeries Springer Monographs in MathematicsEditor: Tokyo : Springer Japan : Imprint: Springer, 2011Descripción: XVI, 320 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9784431539384Tema(s): Mathematics | Functional analysis | Geometry | Mathematics | Geometry | Functional AnalysisFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 516 Clasificación LoC:QA440-699Recursos en línea: Libro electrónicoTipo de ítem | Biblioteca actual | Colección | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras |
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Libro Electrónico | Biblioteca Electrónica | Colección de Libros Electrónicos | QA440 -699 (Browse shelf(Abre debajo)) | 1 | No para préstamo | 377222-2001 |
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.
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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