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...
| Main Authors: | , |
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| Corporate Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Tokyo :
Springer Japan : Imprint: Springer,
2011.
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| Series: | Springer Monographs in Mathematics,
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| Subjects: | |
| Online Access: | Full Text via HEAL-Link |
| 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. |
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| Physical Description: | XVI, 320 p. online resource. |
| ISBN: | 9784431539384 |
| ISSN: | 1439-7382 |
