The Resource Theory of hypergeometric functions, Kazuhiko Aomoto, Michitake Kita ; with an appendix by Toshitake Kohno
Theory of hypergeometric functions, Kazuhiko Aomoto, Michitake Kita ; with an appendix by Toshitake Kohno
Resource Information
The item Theory of hypergeometric functions, Kazuhiko Aomoto, Michitake Kita ; with an appendix by Toshitake Kohno represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Theory of hypergeometric functions, Kazuhiko Aomoto, Michitake Kita ; with an appendix by Toshitake Kohno represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
- Summary
- 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
- Language
-
- eng
- jpn
- eng
- Extent
- 1 online resource (xvi, 317 pages).
- Contents
-
- 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
- Isbn
- 9784431539384
- Label
- Theory of hypergeometric functions
- Title
- Theory of hypergeometric functions
- Statement of responsibility
- Kazuhiko Aomoto, Michitake Kita ; with an appendix by Toshitake Kohno
- Language
-
- eng
- jpn
- eng
- Summary
- 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
- Cataloging source
- GW5XE
- http://library.link/vocab/creatorName
- Aomoto, Kazuhiko
- Dewey number
- 515/.55
- Index
- index present
- Language note
- English
- LC call number
- QA353.H9
- LC item number
- A56 2011
- Literary form
- non fiction
- Nature of contents
-
- dictionaries
- bibliography
- http://library.link/vocab/relatedWorkOrContributorDate
- -1995
- http://library.link/vocab/relatedWorkOrContributorName
- Kita, Michitake
- Series statement
- Springer monographs in mathematics
- http://library.link/vocab/subjectName
-
- Hypergeometric functions
- Hypergeometric functions
- Label
- Theory of hypergeometric functions, Kazuhiko Aomoto, Michitake Kita ; with an appendix by Toshitake Kohno
- Bibliography note
- Includes bibliographical references and index
- Carrier category
- online resource
- Carrier category code
-
- cr
- Carrier MARC source
- rdacarrier
- Color
- multicolored
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
- 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
- Control code
- 733543403
- Dimensions
- unknown
- Extent
- 1 online resource (xvi, 317 pages).
- Form of item
- online
- Isbn
- 9784431539384
- Media category
- computer
- Media MARC source
- rdamedia
- Media type code
-
- c
- Other control number
- 10.1007/978-4-431-53938-4
- http://library.link/vocab/ext/overdrive/overdriveId
- 978-4-431-53912-4
- Specific material designation
- remote
- System control number
- (OCoLC)733543403
- Label
- Theory of hypergeometric functions, Kazuhiko Aomoto, Michitake Kita ; with an appendix by Toshitake Kohno
- Bibliography note
- Includes bibliographical references and index
- Carrier category
- online resource
- Carrier category code
-
- cr
- Carrier MARC source
- rdacarrier
- Color
- multicolored
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
- 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
- Control code
- 733543403
- Dimensions
- unknown
- Extent
- 1 online resource (xvi, 317 pages).
- Form of item
- online
- Isbn
- 9784431539384
- Media category
- computer
- Media MARC source
- rdamedia
- Media type code
-
- c
- Other control number
- 10.1007/978-4-431-53938-4
- http://library.link/vocab/ext/overdrive/overdriveId
- 978-4-431-53912-4
- Specific material designation
- remote
- System control number
- (OCoLC)733543403
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Theory-of-hypergeometric-functions-Kazuhiko/isejvxJO6do/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Theory-of-hypergeometric-functions-Kazuhiko/isejvxJO6do/">Theory of hypergeometric functions, Kazuhiko Aomoto, Michitake Kita ; with an appendix by Toshitake Kohno</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
