00000cmm a22000004a 4500 UP-99796217611212590 Buklod 20230215085534.0 m go j cr |n |||auu|a 110521s2011 xx u | eng d 9784431539384 (eBook) 4431539387 (eBook) (iLib)UPD-00215704401 DML eng DMLUC QA 353 H9 A66 2011eb Aomoto, Kazuhiko. Theory of hypergeometric functions [electronic resource] by Kazuhiko Aomoto, Michitake Kita. Tokyo Springer Japan Springer 2011. 1 electronic resource (xvi, 317 p.) Springer monographs in mathematics 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. IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. 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. Electronic reproduction. New York SpringerLink c2011. Available via World Wide Web through SpringerLink. Hypergeometric functions. Electronic books. Kita, Michitake. Electronic Resource Available for University of the Philippines Diliman via SpringerLink. Click here to access http://dx.doi.org/10.1007/978-4-431-53938-4 FO Monograph UPD DMLR Electronic Resource