Theory of hypergeometric functions /
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| Author / Creator: | Aomoto, Kazuhiko. |
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| Imprint: | Tokyo ; New York : Springer, c2011. |
| Description: | 1 online resource (xvi, 317 p.) |
| Language: | English |
| Series: | Springer monographs in mathematics Springer monographs in mathematics. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8898286 |
| 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: | 1 online resource (xvi, 317 p.) |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9784431539384 4431539387 |