Theory of Hypergeometric Functions [recurso electrónico] / by Kazuhiko Aomoto, Michitake Kita.

Por: Aomoto, Kazuhiko [author.]Colaborador(es): Kita, Michitake [author.] | SpringerLink (Online service)Tipo de material: TextoTextoSeries 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 electrónicoTexto
Contenidos:
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.
En: Springer eBooksResumen: 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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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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