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MARC 21

Theory of Hypergeometric Functions
Tag Description
020$a9784431539384
082$a516
099$aOnline Resource: Springer
100$aAomoto, Kazuhiko.$d1939-
245$aTheory of Hypergeometric Functions$hEB$cby Kazuhiko Aomoto, Michitake Kita.
260$aTokyo$bSpringer Japan
260$c2011.
300$aXVI, 320 pages$bonline resource.
336$atext
338$aonline resource
440$aSpringer Monographs in Mathematics,$x1439-7382
505$a1 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.
520$aThis book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. Starting from an integrand which is a product of powers of polynomials, integrals are explained, in an open affine space, as a pair of twisted de Rham cohomology and its dual over the coefficients of local system. It is shown that hypergeometric integrals generally satisfy a holonomic system of linear differential equations with respect to the coefficients of polynomials and also satisfy a holonomic system of linear difference equations with respect to the exponents. These are deduced from Grothendieck-Deligneâs rational de Rham cohomology on the one hand, and by multidimensional extension of Birkhoffâs classical theory on analytic difference equations on the other.
538$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
700$aKita, Michitake.$eauthor.
710$aSpringerLink (Online service)
830$aSpringer Monographs in Mathematics,
856$uhttp://dx.doi.org/10.1007/978-4-431-53938-4
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