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[ FreeCourseWeb ] Theory of Hypergeometric Functions

Torrent: [ FreeCourseWeb ] Theory of Hypergeometric Functions
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[ FreeCourseWeb.com ] Theory of Hypergeometric Functions

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English | PDF,EPUB | 2011 | 327 Pages | ISBN : 4431539123 | 8.2 MB

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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Added: 2020-01-18 11:03:33
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