| Theory of Hypergeometric Functions Contributor(s): Aomoto, Kazuhiko (Author), Kita, Michitake (Author), Kohno, Toshitake |
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ISBN: 4431539123 ISBN-13: 9784431539124 Publisher: Springer OUR PRICE: $132.99 Product Type: Hardcover - Other Formats Published: May 2011 |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - General - Mathematics | Functional Analysis |
| Dewey: 515.55 |
| LCCN: 2011923079 |
| Series: Springer Monographs in Mathematics |
| Physical Information: 0.8" H x 6.4" W x 9.4" (1.20 lbs) 317 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. 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. |