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 du...

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Detalles Bibliográficos
Autores principales: Aomoto, Kazuhiko, Kita, Michitake, Kohno, Toshitake, Iohara, Kenji
Lenguaje:eng
Publicado: Springer 2011
Materias:
Mathematical Physics and Mathematics
Acceso en línea:https://dx.doi.org/10.1007/978-4-431-53938-4
http://cds.cern.ch/record/1414035
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author Aomoto, Kazuhiko
Kita, Michitake
Kohno, Toshitake
Iohara, Kenji
author_facet Aomoto, Kazuhiko
Kita, Michitake
Kohno, Toshitake
Iohara, Kenji
author_sort Aomoto, Kazuhiko
collection CERN
description 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.
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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2011
publisher Springer
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spelling cern-14140352021-04-22T00:41:12Zdoi:10.1007/978-4-431-53938-4http://cds.cern.ch/record/1414035engAomoto, KazuhikoKita, MichitakeKohno, ToshitakeIohara, KenjiTheory of Hypergeometric FunctionsMathematical Physics and MathematicsThis 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. Springeroai:cds.cern.ch:14140352011
spellingShingle Mathematical Physics and Mathematics
Aomoto, Kazuhiko
Kita, Michitake
Kohno, Toshitake
Iohara, Kenji
Theory of Hypergeometric Functions
title Theory of Hypergeometric Functions
title_full Theory of Hypergeometric Functions
title_fullStr Theory of Hypergeometric Functions
title_full_unstemmed Theory of Hypergeometric Functions
title_short Theory of Hypergeometric Functions
title_sort theory of hypergeometric functions
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-4-431-53938-4
http://cds.cern.ch/record/1414035
work_keys_str_mv AT aomotokazuhiko theoryofhypergeometricfunctions
AT kitamichitake theoryofhypergeometricfunctions
AT kohnotoshitake theoryofhypergeometricfunctions
AT ioharakenji theoryofhypergeometricfunctions

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